Question

x-1/x=2; x^2+1/x^2=

Answer 1

Answer:

Step-by-step explanation:

Find x2−1x2 when

x−1x=32

If it was a plus sign in the squared sum we could do this without solving just by squaring the form we know to be 3/2. But with the minus we might as well solve:

2x2−3x−2=0

(2x+1)(x−2)=0

x=−12 or x=2

x2−1x2=14−4=−114 or x2−1x2=4−14=114

Putting it together, we can’t tell the sign of the difference:

x2−1x2=±154

Check: 2−1/2=3/2.✓4–1/4=15/4✓

−1/2−(1/(−1/2))=3/2.✓1/4−4=−15/4✓

The fact that it came out with ± gives me a hint how to do it without solving:

(x−1x)2=(32)2

x2+1x2−2=9/4

(x2+1x2)2=(17/4)2

x4+1x4=172/16−2

s=x2−1x2

s2=x4+1x4−2=172/16−4=225/16

s=±15/4

hope it helps you

please vote..