2 years ago

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Mathematics

1 answer:

Bingel [31]2 years ago

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Answer:

what exactly is this question

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Square root of 6 minus square root of 7 divided by square root of 6 plus square root of 7

zheka24 [161]

$\frac{ \sqrt{6}- \sqrt{7} }{ \sqrt{6}+ \sqrt{7} } \\ 
 Multiply \ and \ divide \ by \ the \ conjugate. \\ 
 =\frac{ \sqrt{6}- \sqrt{7} }{ \sqrt{6}+ \sqrt{7} } \times \ \frac{ \sqrt{6}- \sqrt{7} }{ \sqrt{6}- \sqrt{7} } \\ 
=$
$\frac{( \sqrt{6}- \sqrt{7})^2 }{ \sqrt{6}^2 - \sqrt{7}^2 }} \\ 
 =\frac{( \sqrt{6}- \sqrt{7})^2 }{-1} \\ 
 =-( \sqrt{6}- \sqrt{7})^2 \\ 
 = -( \sqrt{6}^2-2( \sqrt{6} \sqrt{7}+ \sqrt{7}^2 \\ 
 =-(6 -2 \sqrt{42} +7) \\ 
 =-6+2 \sqrt{42}-7 \\ 
 =-13+2 \sqrt{42} \\ 
Answer: \ -13+2 \sqrt{42}$