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

Question

Find the product of real roots of equation, x2+18 x+30=2 √x2+18 x+45. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

x2+18 x+30 =2 √x2+18 x+45 x2+18 x+30=t t=2 √t+15 t2-4 t-60=0 t=10,-6 put x2+18 x+30=10 put x2+18 x+30=-6 ⇒ x2+18 x+20=0 not possible because LHS so P =20 is (-) at this value

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

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

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

x2+18x+30 =2x2+18x+45​ x2+18x+30=t t=2t+15​ t2−4t−60=0 t=10,−6 put x2+18x+30=10 put x2+18x+30=−6 ⇒x2+18x+20=0 not possible because LHS so P=20 is (−) at this value

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

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