Advertisements
Advertisements
Question
If a + b = 8 and ab = 6, find the value of a3 + b3
Advertisements
Solution
In the given problem, we have to find the value of `a^3 +b^3`
Given `a+b = 8.ab = 6`
We shall use the identity `a^3 + b^3 = (a+b)^3 ab(a+b)`
`a^3 + b^3 = (a+b)^3- 3ab (a+b)`
`a^3 +b^3 = a(8)^3 - 3 3 xx 6 (8)`
`a^3 +b^3 = 512 - 144`
`a^3+b^3 = 368`
Hence the value of i`a^3 +b^3` is 368 .
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(x + 4) (x + 10)
Factorise the following using appropriate identity:
9x2 + 6xy + y2
Evaluate the following using identities:
(2x + y) (2x − y)
Evaluate following using identities:
(a - 0.1) (a + 0.1)
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
Find the following product:
\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
If x = −2 and y = 1, by using an identity find the value of the following
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
If a2 + b2 + c2 − ab − bc − ca =0, then
Find the square of `(3a)/(2b) - (2b)/(3a)`.
Evaluate: (2a + 0.5) (7a − 0.3)
Expand the following:
(a + 3b)2
If `x + (1)/x = 3`; find `x^4 + (1)/x^4`
Simplify:
(4x + 5y)2 + (4x - 5y)2
If `49x^2 - b = (7x + 1/2)(7x - 1/2)`, then the value of b is ______.
Expand the following:
`(1/x + y/3)^3`
Find the following product:
`(x/2 + 2y)(x^2/4 - xy + 4y^2)`
