please answer this 3 questions
Answers
Explanation:
Value of x is –288.
Step-by-step explanation:
\sf{\longrightarrow{\sqrt{1 + \dfrac{x}{289} } \: = 1 \times \dfrac{1}{17}}}⟶
1+
289
x
=1×
17
1
\sf{\longrightarrow{\sqrt{1 + \dfrac{x}{289} } \: = \dfrac{1}{17}}} - - (squaring \: both \: sides)⟶
1+
289
x
=
17
1
−−(squaringbothsides)
\sf{\longrightarrow{\left(\sqrt{1 + \dfrac{x}{289} }\right)^{2} \: = {\left( \: \dfrac{1}{17}\right)}}}^{2}⟶(
1+
289
x
)
2
=(
17
1
)
2
\sf{\longrightarrow{1 + \dfrac{x}{289}} \: = \dfrac{1}{289}}⟶1+
289
x
=
289
1
\sf{\longrightarrow{\dfrac{x}{289}} \: = \dfrac{1}{289} - 1}⟶
289
x
=
289
1
−1
\sf{\longrightarrow{\dfrac{x}{289}} \: = \dfrac{1 - 289}{289}}⟶
289
x
=
289
1−289
\sf{\longrightarrow{\dfrac{x}{289}} \: = \dfrac{ - 288}{289}}⟶
289
x
=
289
−288
\sf{\longrightarrow{ 289x = - 288 \times 289}}⟶289x=−288×289
\sf{\longrightarrow{289x = - 83232}}⟶289x=−83232
\sf{\longrightarrow{x = \dfrac{- 83232}{289}}}⟶x=
289
−83232
\sf{\longrightarrow{x = - 288}}⟶x=−288
Value of x = –288.
___________________
★ Verification:
Put the value of x in LHS,
\sf{\longrightarrow{\sqrt{1 + \dfrac{ - 288}{289}}}}⟶
1+
289
−288
\sf{\longrightarrow{\sqrt{\dfrac{289 + ( - 288)}{289}}}}⟶
289
289+(−288)
\sf{\longrightarrow{\sqrt{\dfrac{1}{289}}}}⟶
289
1
\sf{\longrightarrow{\dfrac{1}{17}}}⟶
17
1
LHS = RHS
Hence verified!