Question

x² + 1/x² - 2- 3x + 3/2
Pls solve quickly. ​

Answer 1

Answer:

Find x2−1x2x2−1x2 when

x−1x=32x−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 3/2.3/2. But with the minus we might as well solve:

2x2−3x−2=02x2−3x−2=0

(2x+1)(x−2)=0(2x+1)(x−2)=0

x=−12x=−12 or x=2x=2

x2−1x2=14−4=−114x2−1x2=14−4=−114 or x2−1x2=4−14=114x2−1x2=4−14=114

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

x2−1x2=±154x2−1x2=±154

Check: 2−1/2=3/2.✓4–1/4=15/4✓<