Question

If a,b and irrational numbers find value of a and b in the r quation √2+√5/√2-√5=a+b√10?

Answer 1

Answer:

Given,

$\dfrac{\sqrt2 + \sqrt5}{\sqrt2 -\sqrt5}=a+b\sqrt{10}$

Simplifying LHS-

$\implies \dfrac{\sqrt2 + \sqrt5}{\sqrt2-\sqrt5} \times\dfrac{\sqrt2 +\sqrt5}{\sqrt2 + \sqrt5} \\\\\\\\\implies \dfrac{(\sqrt2 + \sqrt5)^2}{(\sqrt2)^2 - (\sqrt5)^2}\\\\\\\implies \dfrac{2+5+2\sqrt{5*2}}{2-5}\\\\\\\implies \dfrac{7+2\sqrt{10}}{-3}\\\\\\\implies \dfrac{-7}{3} -\dfrac{2\sqrt{10}}{3}$

Comparing LHS and RHS-

Comparing LHS and RHS-a = -7/3 and b = - 2/3