// //]]>
Get a free home demo of LearnNext

Available for CBSE, ICSE and State Board syllabus.
Call our LearnNext Expert on 1800 419 1234 (tollfree)
OR submit details below for a call back

clear

Question & Answer Forum

Next time you have a doubt while studying, you know where to go. By simply posting your questions on Question & Answer Forum, you can have them answered by academic experts. You can also find related videos and explanations for better understanding.

Can’t find a match Ask?

Syeda answered 1 year(s) ago

If x + 1/x = 3 , then find the value of x6+1/x6.

Assuming the question as (x + 1/x) = 3
Squaring on both the sides we get
(x + 1/x) 2 = 3 2
x 2 +(1/x 2) + 2 = 9
⇒ x 2...

Asked by Neha

Aug 19

  • 4 Answers
  • 30 Likes
  • 103817 Views
Syeda answered 1 year(s) ago

x3 +1/x3 = 110,then x+1/x =

Given x 3+ 1/x 3 =110
Recall that (x+1/x) 3 = x 3+ 1/x 3 + 3(x+1/x)
Let (x+1/x)=a
⇒ a 3 = 110 + 3a
⇒a...

Asked by Raj kishore

Jul 10

  • 3 Answers
  • 4 Likes
  • 57811 Views
Agam answered 1 year(s) , 10 month(s) ago

Factorize x3 - 3x2 - 9x - 5

Great job Meghna, its absolutely correct.

Asked by Meghna

Aug 5

  • 2 Answers
  • 10 Likes
  • 53138 Views
Agam answered 1 year(s) , 10 month(s) ago

If a2+b2+c2-ab-bc-ca=0,prove that a=b=c.

Consider, a 2 + b 2 + c 2 – ab – bc – ca = 0
Multiply both sides with 2, we get
2( a 2 + b 2 + c 2 – ab – bc – ca) = 0...

  • 2 Answers
  • 5 Likes
  • 47479 Views
Kishore answered 5 year(s) , 9 month(s) ago

Factorise: x4 +x2 +1

Consider x 4 + x 2 + 1
            = (x 4 + 2x 2 + 1) – x 2
            = [(x 2) 2 + 2x 2 + 1] – x...

Asked by Sunitha

Aug 19

  • 1 Answer
  • 7 Likes
  • 39381 Views
Syeda answered 1 year(s) ago

If x + y + z = 8 and xy + yz + zx = 20 find the value of x3 + y3 + z3 - 3xyz.

Given x + y + z = 8 and xy + yz + zx = 20
Consider, x + y + z = 8
Squaring on both sides, we get
(x + y + z) 2 = 8 2
x 2 + y 2 + z...

Asked by Meghna

Jul 26

  • 3 Answers
  • 3 Likes
  • 38492 Views
Syeda answered 1 year(s) ago

If x4+1/x4 =119 then find x3-1/x3


Now subtract 2 from both the sides, we get

Cubing on both the sides we get

  • 3 Answers
  • 1 Like
  • 37521 Views
Agam answered 1 year(s) , 10 month(s) ago

If a+b+c=0, then find the value of a2/bc+b2/ca+c2/ab

Given a + b + c = 0
⇒ a 3  + b 3  + c 3  = 3abc  → (1)
Consider, (a 2 /bc) + (b 2 /ca) + (c 2 /ab)
= (a 3  + b 3  + c 3 )/abc
= 3abc/abc = 3   [From (1)]..

Asked by Neha

Aug 31

  • 2 Answers
  • 10 Likes
  • 33970 Views
Ashok K answered 2 year(s) , 5 month(s) ago

If 4x - 4x - 1 = 24 then (2x)x equals what ?

Given 4 x - 4 x - 1 = 24
⇒ 4 x – (4 x/ 4 1) = 24 [Since a m - n = a m / a n]
⇒ 4 x [1...

Asked by Anshu

Oct 7

  • 3 Answers
  • 1 Like
  • 30411 Views
Kishore answered 5 year(s) , 11 month(s) ago

without actually calculating the cubes,find the value of each of the following

Given (28) 3 + (−15) 3 + (−13) 3
Recall that whenever (a+ b + c) = 0, a 3 + b 3 + c 3 = 3abc
Here a = 28, b = −15 and c =...

Asked by Reshma

Jul 10

  • 1 Answer
  • 7 Likes
  • 29448 Views
Agam answered 1 year(s) , 9 month(s) ago

If x=3+2 (under root)2then find the value of:- root x - 1/root x

Given x = 3 + 2√2
⇒ x = 2 + 1 + 2√2
⇒ x = (√2) 2 + 1 2 + 2×√2×1
⇒ x = (√2 + 1) 2
∴ x = (√2 + 1)
⇒(1/x) = 1/ (√2 + 1)
Multiply...

Asked by Vaibhav

Jul 24

  • 2 Answers
  • 0 Like
  • 29289 Views
Agam answered 1 year(s) , 9 month(s) ago

If the polynomial ax3 + 4x2 + 3x - 4 and x3 - 4x + a leave the same remainder

Given ax3 + 4x2 + 3x - 4 and x3 - 4x + a leave the same remainder when divided by x - 3.
Let p(x) = ax3 + 4x2 + 3x - 4 and g(x) = x3 - 4x + a
By remainder theorem, if f(x) is divided by (x − a)...

Asked by Meghna

Jul 23

  • 2 Answers
  • 2 Likes
  • 28900 Views
Agam answered 1 year(s) , 9 month(s) ago

If a = 2 + √3 then find the value of (a - 1/a)

Given a = 2 + √3
⇒ (1/a) = 1 / (2 + √3)
Multiply and divide by (2 − √3)
⇒ (1/a) = (2 − √3) / [(2 + √3)(2 − √3)]
⇒ (1/a) = (2 − √3) / [4 − 3]
⇒ (1/a) = (2 − √3)
∴...

Asked by Meghna

Jul 22

  • 2 Answers
  • 8 Likes
  • 28543 Views
Kishore answered 5 year(s) , 9 month(s) ago

Prove that (a+b+c)3-a3-b3-c3 = 3(a+b)(b+c)(c+a)

Asked by Aakash

Sep 13

  • 1 Answer
  • 7 Likes
  • 26256 Views
Syeda answered 1 year(s) , 9 month(s) ago

If polynomials ax3+3x2-3 and 2x3-5x+a leaves the same remainder

If x2-3x+2 is a factor of poynomial x4-ax3+b then find the value of a and b?

Asked by Akash

May 18

  • 3 Answers
  • 0 Like
  • 26193 Views
Vishnu answered 3 year(s) , 9 month(s) ago

If a + b + c = 7 and ab + bc + ca = 20, find the value of a 2 + b 2 + c 2.

(a+b+c) 2=a 2+b 2+c 2+2ab+2bc+2ca
a 2+b 2+c 2= (a+b+c) 2-2ab-2bc-2ca
a 2+b 2...

Asked by Arjun

Sep 12

  • 5 Answers
  • 3 Likes
  • 25893 Views
Agam answered 1 year(s) , 10 month(s) ago

If two lines intersect then the vertically opposite angles are equal


Given two lines AB and CD intersect each other at the point O.
To prove: ∠1 = ∠3 and ∠2 = ∠4
Proof:
From the figure, ∠1 + ∠2 = 180°  [Linear pair]  → (1)
∠2 + ∠3 = 180°  [...

Asked by Najiha

Sep 3

  • 2 Answers
  • 3 Likes
  • 23267 Views
Agam answered 1 year(s) , 10 month(s) ago

If a + b+ c = 9 and ab + bc + ac = 26 find a2 + b2 + c2.

Given (a + b + c) = 9 and (ab + bc + ca) = 26
(a + b + c) 2  = 9 2
⇒ a 2  + b 2  + c 2  + 2(ab + bc + ca)  = 81
⇒ a 2  + b 2  + c 2  + 2(26)  = 81
⇒ a 2  + b 2  + c 2  + 52  = 81...

Asked by Meghna

Jul 26

  • 2 Answers
  • 4 Likes
  • 22915 Views
Kishore answered 5 year(s) , 10 month(s) ago

If 2 to the power X = 3 to the power Y = 6 to the power - Z.

Given 2 x = 3 y = 6 –z
Let 2 x = 3 y = 6 –z = k
Consider, 2 x = k
  → (1)...

  • 1 Answer
  • 2 Likes
  • 22565 Views
Agam answered 9 month(s) , 28 day(s) ago

1.find a quadratic polynomial,the sum and product of whose zeroes are 0 and root5 respectively

Sol :
α, β are zeros of the quadratic polynomial then sum and product of whose zeroes are 0 and √5 respectively.
 ∴   α + β = 0   αβ = √5.
α, β are zeros of the quadratic polynomial then...

Asked by Muskaan

Apr 27

  • 2 Answers
  • 2 Likes
  • 21024 Views
Like NextGurukul? Also explore our advanced self-learning solution LearnNext
Offered for classes 6-12, LearnNext is a popular self-learning solution for students who strive for excellence
Explore
Animated Video
lessons
All India
Test Series
Interactive Video
Experiments
Best-in class
books

Join India's most happening

Educational community