Question

if ( a+ 5,4) =( 2+b, 2) then find a and b​

Answer 1

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You are asking $(a+b):(a-b)=5:3,$

then find the value of :-

$(a^2+b^2):(a^2-b^2)$

$\dfrac {a+b}{a-b} = \dfrac {5}{3}$

Applying componendo & dividendo

$\dfrac {a+b+a-b}{a+b-a+b} = \dfrac {5+3}{5-3}$

$\dfrac {2a}{2b}=\dfrac {8}{2}$

$\dfrac {a}{b}=\dfrac {4}{1}$

Finding

$\dfrac {a^2}{b^2}$

$(\dfrac {a}{b})^2 = (\dfrac{4}{1})^2$

$\dfrac {a^2}{b^2} = \dfrac {16}{1}$

Applying componendo & dividendo

$\dfrac {a^2+b^2}{a^2-b^2} = \dfrac {16+1}{16-1}$

$\dfrac{a^2+b^2}{a^2-b^2} = \dfrac{17}{15}$

$\boxed{17:15}$

$\\ hope \: it \: helps \:$

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