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Syeda
answered
1 year(s)
, 8 month(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}...

- 4 Answers
- 30 Likes
- 94777 Views

Syeda
answered
1 year(s)
, 8 month(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
- 51181 Views

Agam
answered
1 year(s)
, 6 month(s) ago

Factorize x3 - 3x2 - 9x - 5

Great job Meghna, its absolutely correct.

- 2 Answers
- 8 Likes
- 43166 Views

Agam
answered
1 year(s)
, 6 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...

Asked by Mohammed furqaan

Aug 23

- 2 Answers
- 5 Likes
- 40587 Views

Syeda
answered
1 year(s)
, 8 month(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

Asked by Smritishraddha

Aug 27

- 3 Answers
- 1 Like
- 32828 Views

Syeda
answered
1 year(s)
, 8 month(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...

- 3 Answers
- 3 Likes
- 32435 Views

Kishore
answered
5 year(s)
, 5 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...

- 1 Answer
- 6 Likes
- 31473 Views

Agam
answered
1 year(s)
, 6 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)]..

- 2 Answers
- 9 Likes
- 28735 Views

Agam
answered
1 year(s)
, 5 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...

- 2 Answers
- 0 Like
- 26973 Views

Ashok K
answered
2 year(s)
, 1 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...

- 3 Answers
- 1 Like
- 26382 Views

Kishore
answered
5 year(s)
, 7 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 =...

- 1 Answer
- 6 Likes
- 26056 Views

Agam
answered
1 year(s)
, 5 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)...

- 2 Answers
- 2 Likes
- 24821 Views

Vishnu
answered
3 year(s)
, 5 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}...

- 5 Answers
- 3 Likes
- 23720 Views

Agam
answered
1 year(s)
, 5 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)

∴...

- 2 Answers
- 8 Likes
- 22991 Views

Syeda
answered
1 year(s)
, 5 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?

- 3 Answers
- 0 Like
- 22701 Views

Kishore
answered
5 year(s)
, 5 month(s) ago

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

- 1 Answer
- 6 Likes
- 21268 Views

Agam
answered
1 year(s)
, 6 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...

- 2 Answers
- 4 Likes
- 19144 Views

Agam
answered
5 month(s)
, 26 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...

- 2 Answers
- 2 Likes
- 19094 Views

Agam
answered
1 year(s)
, 6 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° [...

- 2 Answers
- 3 Likes
- 17618 Views

Kishore
answered
5 year(s)
, 6 month(s) ago

If the complement of an angle is one-third of its supplement, find the angle.

Let the angle be x

complement of x is (90 − x)°

supplement of x is (180 − x)°

Given (90 − x)° = (1/3) × (180 − x)°

⇒ 270° − 3x = 180°− x

⇒ 270° − 180° = 3x − x

⇒...

- 1 Answer
- 1 Like
- 17436 Views

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