Question

if x =√3+√2/√3-√2, find the value of x²​

Answer 1

Answer:

Step-by-step explanation:

Consider x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}

We first rationalize the denominator  by multiply and divide by {\sqrt{3}+\sqrt{2}}

we get,

x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\times \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}

Simplify, we get,

x=\frac{(\sqrt{3}+\sqrt{2})^2}{(\sqrt{3})^2-(\sqrt{2})^2}\\\\ x=\frac{(\sqrt{3}+\sqrt{2})^2}{3-2}\\\\ x=(\sqrt{3}+\sqrt{2})^2

Thus, squaring both side we get,

x^2=((\sqrt{3}+\sqrt{2})^2)^2

using algebraic identity (a+b)^2=a^2+b^2+2ab , we have,