Question

Rationalising the denominator and find the value of a and b. (11+√14) / (11-√14) = a+b√14​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ \frac{11 + \sqrt{14} }{11 - \sqrt{14} } = a + b \sqrt{14} }$

EVALUATION

$\displaystyle \sf{ \frac{11 + \sqrt{14} }{11 - \sqrt{14} } = a + b \sqrt{14} }$

$\displaystyle \sf{ \implies \frac{(11 + \sqrt{14})(11 + \sqrt{14}) }{(11 + \sqrt{14})(11 - \sqrt{14}) } = a + b \sqrt{14} }$

$\displaystyle \sf{ \implies \frac{{(11 + \sqrt{14})}^{2} }{ {(11)}^{2} - {( \sqrt{14} )}^{2} } = a + b \sqrt{14} }$

$\displaystyle \sf{ \implies \frac{121 + 22 \sqrt{14} + 14 }{ 121 - 14} = a + b \sqrt{14} }$

$\displaystyle \sf{ \implies \frac{135 + 22 \sqrt{14} }{ 107} = a + b \sqrt{14} }$

$\displaystyle \sf{ \implies \frac{135 }{ 107} + \frac{22}{107} \sqrt{14} = a + b \sqrt{14} }$

FINAL ANSWER

$\displaystyle \sf{a = \frac{135}{107} \: , \: b = \frac{22}{107} }$

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