Answer:

{\fcolorbox{aqua}{blue}{\orange{Question\:Provided\:»»}}}

QuestionProvided»»

\sqrt{(x+6)^2+5^2}+\sqrt{(x-6)^2+11^2}

(x+6)

2

+5

2

+

(x−6)

2

+11

2

{\fcolorbox{aqua}{orange}{\blue{Here's\:the\:Answer\:»»}}}

Here’stheAnswer»»

\sf{\implies\sqrt{ ( x + 6 )² + 5² } \:+\: \sqrt{ ( x - 6 )² + 11² } \:=\: 0} ⟹

(x+6)²+5²

+

(x−6)²+11²

=0

\sf{\implies\sqrt{ ( x + 6 )² + 5² } \:=\: - \sqrt{ ( x - 6 )² + 11² }}⟹

(x+6)²+5²

=−

(x−6)²+11²

\sf{\implies \bigg( \sqrt{ ( x + 6 )² + 5² } \bigg)^{2} \:=\: \bigg( - \sqrt{ ( x - 6 )² + 11² } \bigg)^{2} }⟹(

(x+6)²+5²

)

2

=(−

(x−6)²+11²

)

2

\implies \sf{ ( x + 6 )² + 5² \:=\: ( x - 6 )² + 11² } ⟹(x+6)²+5²=(x−6)²+11²

\sf{ \implies x² + 12x + 36 + 25 \:=\: x² - 12x + 36 + 121 }⟹x²+12x+36+25=x²−12x+36+121

\sf{\implies x² - x² + 12x + 12x + 61 \:=\: 36 + 121 }⟹x²−x²+12x+12x+61=36+121

\implies \sf{x² - x² + 12x + 12x + 61 \:=\: 157 } ⟹x²−x²+12x+12x+61=157

\implies \sf{ 24x + 61 \:=\: 157 }⟹24x+61=157

\implies \sf{ 24x \:=\: 157 - 61 }⟹24x=157−61

\implies \sf{ x \:=\: \dfrac{96}{24}}⟹x=

24

96

\implies \sf{\green{ x \:=\: 4 }}⟹x=4

ㅤㅤㅤ \therefore ∴ x = 4

__________________________

Formula used :

\boxed{\sf{\orange{( a + b )² \:=\: a² + 2ab + b² }}}

(a+b)²=a²+2ab+b²

\boxed{\sf{\orange{( a - b )² \:=\: a² - 2ab + b² }}}

(a−b)²=a²−2ab+b²

ㅤㅤㅤ

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