Question

$if \sqrt{ \frac{196}{7 } } + \sqrt{ \frac{900}{x} } = 4 \: find \: the \: value \: of \: x$
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Answer 1

Answer:

$\sqrt{ \frac{196}{7} } + \sqrt{ \frac{900}{x} } = 4 \\ \\ \\ \\ = > \frac{14}{ \sqrt{7} } + \frac{30}{ \sqrt{x} } = 4 \\ \\ = > 14 \sqrt{x} + 30 \sqrt{7} = \sqrt{7} . \sqrt{x} .4 \\ \\ \\ = > 14 \sqrt{x} - \sqrt{7x} + 30 \sqrt{7} = 0 \\ \\ = > \sqrt{x} (14 - \sqrt{7} ) = - 30 \sqrt{7} \\ \\ = > \sqrt{x} = \frac{ - 30 \sqrt{7} }{14 - \sqrt{7} } \\ \\ x = \frac{6300}{169 + 7 - 28 \sqrt{7} } \\ \\ \\ = > \frac{6300}{176 - 28 \sqrt{7} } \\ \\ \\ = > \frac{6300}{176 - 28 \times 2.6} \\ \\ \\ = > \frac{6300}{101.2}$

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Answer 2

$\huge{ \overbrace{ \underbrace{\color{white}{ \fcolorbox{cyan}{black}{Answer:-}}}}}$

$\bf{ \red{ (i)}} \: \sqrt{ \frac{196}{7} } + \sqrt{ \frac{900}{x} } = 4 \\ \bf or, \: \sqrt{ \frac{ \cancel{196}}{ \cancel{7}} } + \frac{30}{ \sqrt{x} } = 4 \\ \bf or, \: \sqrt{28} + \frac{30}{ \sqrt{x} } = 4 \\ \bf or, \: \frac{30}{ \sqrt{x} } = 4 - \sqrt{28} \\ \bf or, \: \sqrt{x } = \frac{30}{4 - \sqrt{28} } \\ \bf or, \: \sqrt{x} = \frac{15}{2 - \sqrt{7} } \\ \bf or, \: x = \frac{225}{4 - 4 \sqrt{7 } + 7 } \\ \bf or, \: x = \frac{225}{11 - 4 \sqrt{7} }$