Question

Daca √3 *x +√5 *y=4 si √5*x +√3*y=12,atunci $\frac{x-y}{ \sqrt{5} + \sqrt{3} }$ este egal cu .........

Answer 1

√3·x+√5·y=4
√5·x+√3·y=12
Scazand cele doua relatii obtinem
√5·x+√3·y-√5·y-√3·x=8 ⇔
√5(x-y)+√3(x-y)=8 ⇔
(x-y)(√5+√3)=8 ⇔
x-y=8 /√5+√3
x-y /√5+√3=
8 /(√5+√3)²=8 /5+2√15+3=8 /8+2√15=8 /2(4+√15)=4 /4+√15;