Question

X and y are two non-zero real numbers such that: x²-y²=15 and x+y=3√5. then x-y=

A. √15
B. √5
C. -3√5​

Answer 1

`(x-y)=√(5)`

Explanation:

`We\ are\ given\ that:\\x^2-y^2=15\\x+y=3 √(5)\\Now,\\We\ know\ that,\\If\ x\ and\ y\ are\ two\ real\ numbers,\\Then:\\(x+y)(x-y)=x^2-y^2\\Here,\\Substituting\ (x+y)=3√(5)\ in\ the\ LHS\ and\ (x^2-y^2)=15\ in\ the\ RHS,\\(x+y)(x-y)=x^2-y^2\\3√(5) (x-y)= 15\\Hence,\\(x-y)=(15)/(3√(5) ) \\(x-y)=(5*3)/(3√(5) )\\(x-y)=(5)/(√(5) ) [Cancelling\ 3\ from\ the\ numerator\ and\ denominator]\\(x-y)=(√(5)*√(5) )/(√(5) )\\(x-y)=√(5)`