Question

$\sqrt{1 + \frac{x}{289} } \: = 1 \times \frac{1}{17 } \: them \: x \: =$
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Answer 1

Answer:

Value of x is –288.

Step-by-step explanation:

$\sf{\longrightarrow{\sqrt{1 + \dfrac{x}{289} } \: = 1 \times \dfrac{1}{17}}}$

$\sf{\longrightarrow{\sqrt{1 + \dfrac{x}{289} } \: = \dfrac{1}{17}}} - - (squaring \: both \: sides)$

$\sf{\longrightarrow{\left(\sqrt{1 + \dfrac{x}{289} }\right)^{2} \: = {\left( \: \dfrac{1}{17}\right)}}}^{2}$

$\sf{\longrightarrow{1 + \dfrac{x}{289}} \: = \dfrac{1}{289}}$

$\sf{\longrightarrow{\dfrac{x}{289}} \: = \dfrac{1}{289} - 1}$

$\sf{\longrightarrow{\dfrac{x}{289}} \: = \dfrac{1 - 289}{289}}$

$\sf{\longrightarrow{\dfrac{x}{289}} \: = \dfrac{ - 288}{289}}$

$\sf{\longrightarrow{ 289x = - 288 \times 289}}$

$\sf{\longrightarrow{289x = - 83232}}$

$\sf{\longrightarrow{x = \dfrac{- 83232}{289}}}$

$\sf{\longrightarrow{x = - 288}}$

Value of x = –288.

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★ Verification:

Put the value of x in LHS,

$\sf{\longrightarrow{\sqrt{1 + \dfrac{ - 288}{289}}}}$

$\sf{\longrightarrow{\sqrt{\dfrac{289 + ( - 288)}{289}}}}$

$\sf{\longrightarrow{\sqrt{\dfrac{1}{289}}}}$

$\sf{\longrightarrow{\dfrac{1}{17}}}$

LHS = RHS

Hence verified!

Answer 2

Given :-

$\bf\sqrt{1+\dfrac{x}{289}} = 1\times\dfrac{1}{17}$

To Find :-

Value of x

Solution :-

$\sf \sqrt{1+\dfrac{x}{289}} = \dfrac{1\times1}{17}$

$\sf \sqrt{1+\dfrac{x}{289}} = \dfrac{1}{17}$

Squaring both sides will give

$\sf\bigg(\sqrt{1+\dfrac{x}{289}}\bigg)^2=\bigg(\dfrac{1}{17}\bigg)^2$

$\sf \bigg(1+\dfrac{x}{289}\bigg)=\dfrac{1}{289}$

$\sf \dfrac{289+x}{289}=\dfrac{1}{289}$

As bases are equal. So, we may cancel them

$\sf 289+x=1$

$\sf x=1-289$

$\sf x=-288$

Henceforth

Value of x is -288