Question

can I get the answer for this fast??​

Answer 1

x²+1/x²=7

→x²+1/x²=7 ,find the value of 7x³+8x−7/x³−8/x

7x³+8x−7/x³−8/x =7x³−7/x³+8/x −8/x

=7(x³−1/x³)+8(1/x −1/x )

=7(x−1/x)(x²+1/x²+1) +8(1/x −1/x ) Factorizing (x³−1/x³)

=7(x−1/x)(7+1) +8(1/x −1/x ) =56(x−1/x) +8(1/x −1/x ) =64(x−1/x) Substituting the value of x²+1/x²=7

To calculate the value of (x−1/x), we use

x²+1/x²=7

→x²+1/x²−2=7−2 subtract 2 on both sides to make the L H S a perfect square of (x−1/x)

→(x−1/x)² = 5

→(x−1/x) = ±√5

Hence

7x³+8x−7/x³−8/x

=64(x−1/x)

=64(±√5)=±64√5