Question

if a+b=7andab=6find a2-b2​

Answer 1

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Given   $a+b=7,ab=6$

$=>b=\frac{6}{a}$

Now sub. b=6/a in 1st equation.

  $a+\frac{6}{a}=7\\\\ =>a^2+6=7a\\\\=>a^2-7a+6=0\\\\=>a^2-a-6a+6=0\\\\=>a(a-1)-6(a-1)=0\\\\=>(a-1)(a-6)=0\\\\=>a=1,a=6$

Sub. a=1 , a=6 in eq. we get b=6 , b=1

So ,

    $a^2-b^2=6^2-1^2=36-1=35\\\\[or]a^2-b^2=1^2-6^2=1-36=-35$

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