Question

If(√14/√7-2)-(√14/√7+2)=a√7+b√2 find the values of a and b where a and b are rational numbers​

Answer 1

Answer:

• a = 4/3 and b = 0

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Given expression:

$\dfrac{\sqrt{14} }{\sqrt{7}-2} -\dfrac{\sqrt{14} }{\sqrt{7}+2}$

Simplify it in steps:

Step 1

Bring both fractions into common denominator:

$\dfrac{\sqrt{14} (\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} - \dfrac{\sqrt{14} (\sqrt{7}-2)}{(\sqrt{7}-2)(\sqrt{7}+2)}$

Step 2

Simplify:

$\dfrac{\sqrt{14} ((\sqrt{7}+2) - (\sqrt{7}-2))}{(\sqrt{7}-2)(\sqrt{7}+2)} =$

$\dfrac{\sqrt{14} (\sqrt{7}+2 - \sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} =$

$\dfrac{4\sqrt{14} }{(\sqrt{7}-2)(\sqrt{7}+2)} =$

$\dfrac{4\sqrt{14} }{(\sqrt{7})^2-2^2} =$

$\dfrac{4\sqrt{14} }{7-4} =$

$\dfrac{4}{3} \sqrt{14} }$

Step 3

Compare the result with given expression to get:

• a = 4/3 and b = 0