Question

If f is a real valued function given by f(x) = 27x³ + 1/x³ and "a" and "b" are roots of 3x + 1/x = 12, then prove that f(b) = -10.

No spams!!
| Class XI | Relations And Functions |​

Answer 1

Correct Question

If f is a real valued function given by f(x) = 27x³ + 1/x³ and "a" and "b" are roots of 3x + 1/x = 2, then prove that f(b) = -10.

Solution

Given that 'a' and 'b' are roots of 3x + 1/x = 2

→ 3b + 1/b = 2

We have to find f(b) when f(x) = 27x³ + 1/x³

Now,

3b + 1/b = 2

Cubing both sides,

(3b + 1/b)³ = 2³

→ (3b)³ + (1/b)³ + 3(3b)(1/b)(3b + 1/b) = 2³

→ 27b³ + 1/b³ + 9(3b + 1/b) = 8

→ 27b³ + 1/b³ + 9(2) = 8 (Since 3b + 1/b = 2)

→ 27b³ + 1/b³ + 18 = 8

→ 27b³ + 1/b³ = -10

Now,

f(x) = 27x³ + 1/x³

→ f(b) = 27b³ + 1/b³

Hence, f(b) = -10.

Answer 2

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CORRECT QUESTION :

If f is a real valued function given by f(x) = 27x³ + 1/x³ and "a" and "b" are roots of 3x + 1/x = 2, then prove that f(b) = -10.

If f is a real valued function given by f(x) = 27x³ + 1/x³ and "a" and "b" are roots of 3x + 1/x = 2, then prove that f(b) = -10.No spams!!

If f is a real valued function given by f(x) = 27x³ + 1/x³ and "a" and "b" are roots of 3x + 1/x = 2, then prove that f(b) = -10.No spams!!| Class XI | Relations And Functions |

CONCEPT USED :

Relations and functions.

Class XI

SOLUTION :

f(x) = 27x³ + 1/x³ and "a" and "b" are roots of 3x + 1/x = 2.

{ 3 x + 1 / x } ^ 3 = { 2 } ^ 3

=> 27 X ^ 3 + 1 / x ^ 3 + 3 { 3 X + 1 / x } = 8

Substituting values of ( 3x + 1 / x ) and equating..

=.> 27 X ^ 3 + 1 / X ^ 3 = - 10

This is f ( b )

Hence proved..........