Question

Daca x-y=9 si xy=10 atunci x la puterea a doua + y la puterea a doua este egal cu ....?
Va rog ajutati-ma!

Answer 1

x=y+9;
x·y=10
⇒[y+9]·y=10
⇒y²+9y=10
⇒y=1[singura solutie];
⇒1²+9·1=1+9=10;
⇒x=1+9
⇒x=10;
⇒x²+y²
⇒10²+1²
⇒100+1⇒101;

Answer 2

x-y=9 |²
(x-y)²=81
x²-2xy+y²=81
x²+y²=81+2xy
x²+y²=81+2*10
x²+y²=81+20
x²+y²=101