If x +1 over x=2, then find the value of (x⁴ +4 over (x)⁴)(x³- 4 over x³).

If x +1 over x=2, then find the value of (x⁴ +4 over…

If $x +{{1} \over x}=2,$ then find the value of $(x^4 +{{4} \over (x)^4})(x^3- {{4} \over x^3}).$

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. -15.

Given that

$x +{{1} \over x}=2$

Solving for x we get x = 1

Substituting the value of x in the given expression

$(x^4 +{{4} \over (x)^4})(x^3- {{4} \over x^3})$ = (1 + 4)(1 - 4) = -15

Hence the value of the given expression is -15.