Question

If x squared minus 14x plus 49/x squared minus 49=3/17 find the value of x

Answer 1

$\bold{\blue{\boxed{\bigstar{\bf{QUESTION}}}}}$

$→ {\purple{\sf{\frac{ {x}^{2} - 14x + 49}{ {x}^{2} - 49 } = \frac{3}{17}}}}$

$</p><h2></h2><p>{\blue{\boxed{\bigstar{\bf{SOLUTION}}}}}$

$&#8594; {\purple{\sf{\frac{ {x}^{2} - 2 \times 7 \times x + {7}^{2} }{ {x}^{2} - {7}^{2} } = \frac{3}{17}}}}$

$&#8594;{\purple{\sf{ \frac{ {( x - 7}^{2}) }{(x - 7)(x + 7)} = \frac{3}{17}}}}$

${\blue{\boxed{\bf{\bigstar{CROSS\: MULTIPLICATION}}}}}$

$&#8594;{\purple{\sf{(x-7)×17=3×(x+7)}}}$

$&#8594;{\purple{\sf{17x-119=3x+21}}}$

$&#8594;{\purple{\sf{17x-3x=21+119}}}$

$&#8594;{\purple{\sf{14x=140}}}$

$&#8594;{\purple{\sf{x = \frac{</p><p>140}{14} = 10}}}$

$&#8594;{\purple{\boxed{\sf{x=10}}}}$

${\blue{\boxed{\bf{\bigstar{VERIFICATION}}}}}$

$&#8594;{\purple{\sf{\frac{ {10}^{2} - 14 \times (10) + 49 }{ {10}^{2}-49 }}}}$

$&#8594;{\purple {\sf{\frac{100 - 140 + 49}{100 - 49}}}}$

$&#8594; {\purple{\sf{\frac{3 \times 3}{17 \times 3}}}}$

$&#8594;{\purple{\sf{ \frac{3}{17}}}}$

${\blue{\boxed{\sf{\bigstar{WE\:GET}}}}}$

${\purple{\boxed{\sf{R.H.S=L.H.S}}}}$

________________

Answer 2

$\bf{\underline{\underline{Question}}}$

IF:-

$\bf{\frac{x^{2}-14x+49}{x^{2}-49}=\frac{3}{17}}$

Find the value of x.

$\bf{\underline{\underline{Solution}}}$

$\bf{\frac{x^{2}-14x+49}{x^{2}-49}=\frac{3}{17}}$

$\bf{\frac{x^{2}-2 \times 7 \times x+49}{x^{2}-7^{2}}=\frac{3}{17}}$

$\bf{\frac{(x-7)^{\cancel2}}{(\cancel x- \cancel 7)(x+7)}=\frac{3}{17}}$

$\bf{(x-7)\times 17}={3\times(x+7)}$

$\bf{17x-119= 3x+21}$

$\bf{17x-3x= 21+119}$

$\bf{14x= 140}$

$\bf{x}= \cancel \frac{140}{14}$

$\bf{\boxed{x\:=\:10}}$

$\bf{\underline{\underline{Thanks}}}$