Question

Find a and b : root 7 - 2 upon root 7 + 2 = a root 7 + b

Answer 1

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Answer 2

The correct answer is a = $\frac{-4}{3}$ and b = $\frac{11}{3}$.

Given: The equation = $\frac{\sqrt{7}-2 }{\sqrt{7}+2 } =a\sqrt{7}+b$.

To Find: Value of a and b.

Solution:

$\frac{\sqrt{7}-2 }{\sqrt{7}+2 } =a\sqrt{7}+b$

Rationalize the LHS.

$\frac{\sqrt{7}-2 }{\sqrt{7}+2 } *\frac{\sqrt{7}-2 }{\sqrt{7}-2 }$

= $\frac{(\sqrt{7}-2)^{2} }{(\sqrt{7})^{2} -(2)^{2} }$

= $\frac{7+4-4\sqrt{7} }{7-4}$

= $\frac{11-4\sqrt{7} }{3}$

= $\frac{11}{3}+(-\frac{4}{3}\sqrt{7} )$

Hence, the value of a is $\frac{-4}{3}$ and the value of b is $\frac{11}{3}$.

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