Question

10- Se x-y=1 e x.y=30 o valor da expressão x^2-y^2 é:​

Answer 1

$\large\boxed{\begin{array}{l}\sf x-y=1~x\cdot y=30\\\sf (x-y)^2=x^2-2xy+y^2\\\sf1^2=x^2+y^2-2\cdot30\\\sf x^2+y^2-60=1\\\sf x^2+y^2=61.\\\sf (x+y)^2=x^2+y^2+2xy\\\sf (x+y)^2=61+2\cdot30\\\sf (x+y)^2=61+60\\\sf (x+y)^2=121\\\sf (x+y)=\sqrt{121}\\\sf x+y=11\\\sf x^2-y^2=(x+y)\cdot(x-y)\\\sf x^2-y^2=11\cdot1\\\sf x^2-y^2=11\end{array}}$