Question

a) Daca x+1 supra x=6, calcaulati x-1 supra x.
b) Daca x-1 supra x=4, calculati x+1 supra x.

Answer 1

Explicație pas cu pas:

x+ 1/x=6=>x²+2x*1/x+1/x²=36=>x²+2+1/x²=36=>x²+1/x²=34

=> x²+1/x²-2=32=>(x-1/x)²=32=>x-1/x=4V2 sau x-1/x=-4V2

x-1/x=4=>x²-2+1/x²=16 (am ridicat x+1/x la patrat) =>

x²+1/x²=18=>x²+2+1/x²=20=>(x+1/x)²=20=>x+1/x=2V5 sau x+1/x=-2V5