Question

$\sqrt{5} + \sqrt{5 - x} \div \sqrt{5} - \sqrt{5 - x } = 3$
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Answer 1

Question :-

Solve for "x"

$\frac{ \sqrt{5} + \sqrt{5 - x} }{ \sqrt{5} - \sqrt{5 - x} } = 3$

Answer :-

$\rightarrow \boxed{\: x = - \frac{25}{4} } \:$

Explanation :-

we have ,

$\frac{ \sqrt{5} + \sqrt{5 - x} }{ \sqrt{5} - \sqrt{5 - x} } = 3 \\ \: \\ \rightarrow \frac{ \sqrt{5} + \sqrt{5 - x} }{ \sqrt{5} - \sqrt{5 - x} } \bigg( \frac{ \sqrt{5} + \sqrt{5 - x} }{ \sqrt{5} + \sqrt{5 - x} } \bigg) = 3 \\ \\ \rightarrow \: \frac{ {( \sqrt{5} + \sqrt{5 - x}) }^{2} }{5 - 5 + x} = 3 \\ \\ \rightarrow \: 5 + 5 - x + 2 \sqrt{5} \sqrt{5 - x} = 3x \\ \\ \rightarrow \: 2 \sqrt{5( 5 - x)} = 4x + 10 \\ \\ \sf{ squaring \: on \: both \: sides \: } \\ \\ \rightarrow \: 4(25 - 5x) = 16 {x}^{2} + 100 + 80x \\ \\ \rightarrow \: 100 - 20x = 16 {x}^{2} + 80x + 100 \\ \\ \rightarrow \: 16 {x}^{2} + 100x = 0 \\ \\ \rightarrow \: 16 {x}^{2} = - 100x \\ \\ \rightarrow \boxed{\: x = - \frac{25}{4} }$

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