Question

8^2-(6+x)^2=3^2-x^2 Find x

Answer 1

Answer:

x = -19/12

Step-by-step explanation:

==: 8² - (6+x)² = 3² - x²

==: 64 - (36 + x² + 12x) = 9 - x²

==: 64 - 36 - x² - 12x = 9 - x²

==: 12x = 9 - 64 + 36

==: 12x = -19

==: x = -19/12

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Answer 2

Answer:

x = $\dfrac{19}{12}$

Given:

$\\\\{8}^{2} - {(6 + x)}^{2} = {3}^{2} - {x}^{2}$

To Find:

Value of x.

Answer:

Explanation:

${8}^{2} - {(6 + x)}^{2} = {3}^{2} - {x}^{2}$

We know that,

$(a + b)^{2} = {a}^{2} + {b}^{2} + 2ab$

$64 - 36 - {x}^{2} - 12x = 9 - {x}^{2} \\ \\ 28 - {x}^{2} + {x}^{2} + 12x - 9 = 0 \: \: \: \\ \\ - 12x + 19 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ - 12x = - 19 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x = \dfrac{19}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Proof:

$64 - \left(6 + \dfrac{19}{12} \right)^{2} = 9 - \left( \dfrac{19}{12} \right)^{2} \\ \\ 64 - {\left( \dfrac{91}{12} \right)}^{2} = 9 - \dfrac{361}{144} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ 64 - \dfrac{8281}{144} = 9 - \dfrac{361}{144} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dfrac{9216 - 8281}{144} = \dfrac{1296 - 361}{144} \: \: \: \: \: \: \: \: \: \\ \\ \dfrac{935}{144} = \dfrac{935}{144} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence Proved.