Question

please answer this question​

Answer 1

GIVEN :-

$\\ \red \bigstar \: \displaystyle \tt \: x = \dfrac{ \sqrt{0.2304 } + \sqrt{0.1764} }{ \sqrt{0.2304} - \sqrt{0.1764} }$

TO FIND :-

$\\ \red \bigstar \: \displaystyle \tt \: The \: value \: of \: "x" \: .$

SOLUTION :-

$\\ \red \bigstar \: \displaystyle \tt \: x = \dfrac{ \sqrt{0.2304 } + \sqrt{0.1764} }{ \sqrt{0.2304} - \sqrt{0.1764} }$

$: \implies \: \displaystyle \tt x = \dfrac{ \sqrt{(0.48) ^{2} } + \sqrt{(0.42) ^{2} } }{ \sqrt{(0.48) ^{2} } - \sqrt{(0.42) ^{2} } }$

$: \implies \: \displaystyle \tt x = \dfrac{0.48 + 0.42}{0.48 - 0.42}$

$: \implies \: \displaystyle \tt x = \cancel\dfrac{0.9}{0.06}$

$: \implies \: \boxed{ \red{ \displaystyle \tt x = 15}}$

$\underline{ \underline{ \displaystyle \tt \therefore \: The \: required \: value \: of \: x \: \: is \: 15. }}$

VERIFICATION :-

$\\ \red \bigstar \: \displaystyle \tt \: x = \dfrac{ \sqrt{0.2304 } + \sqrt{0.1764} }{ \sqrt{0.2304} - \sqrt{0.1764} }$

$: \implies \: \displaystyle \tt 15 = \dfrac{ \sqrt{(0.48) ^{2} } + \sqrt{(0.42) ^{2} } }{ \sqrt{(0.48) ^{2} } - \sqrt{(0.42) ^{2} } }$

$: \implies \: \displaystyle \tt 15 = \dfrac{0.48 + 0.42}{0.48 - 0.42}$

$: \implies \: \displaystyle \tt 15 = \cancel\dfrac{0.9}{0.06}$

$: \implies \: \boxed{ \red{ \displaystyle \tt 15 = 15}}$

L.H.S = R.H.S

HENCE VERIFIED ✅