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  4. Find the product of real roots of equation, x2+18 x+30=2 √x2+18 x+45.

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Q. Find the product of real roots of equation, $x^{2}+18 x+30=2 \sqrt{x^{2}+18 x+45}$.

Complex Numbers and Quadratic Equations

Solution:

$x^{2}+18 x+30$
$=2 \sqrt{x^{2}+18 x+45}$
$x^{2}+18 x+30=t$
$t=2 \sqrt{t+15}$
$t^{2}-4 t-60=0$
$t=10,-6$
put $x^{2}+18 x+30=10$
put $x^{2}+18 x+30=-6$
$\Rightarrow x^{2}+18 x+20=0$
not possible because $LHS$
so $P =20 $ is $(-)$ at this value