Question

solve for x:9x2+9(p+q)+(2p2+5pq+2q2)=0

Answer 1

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Answer 2

Answer:

Here, the given equation is,

$9x^2 + 9(p+q)x + (2p^2+ 5pq + 2q^2 ) = 0$

⇒ $9x^2 + 9(p+q)x + 2p^2 + 4pq + pq + 2q^2 = 0$

⇒ $9x^2 + 9(p+q)x + 2p(p+2q)+q(p+2q) = 0$

⇒ $9x^2 + 9(p+q)x + (2p+q) (p+2q) = 0$

⇒ $x^2 + (p+q)x +\frac{(2p+q)(p+2q)}{9} = 0$

⇒ $x^2 + \frac{2p+q}{3}x+\frac{p+2q}{3}x + \frac{(2p+q)(p+2q)}{9}=0$

⇒ $x(x+\frac{2p+q}{3})+\frac{p+2q}{3}(x+\frac{2p+q}{3})=0$

⇒ $(x+\frac{2p+q}{3})(x+\frac{p+2q}{3})=0$

If $x+\frac{2p+q}{3} = 0\implies x = -(\frac{2p+q}{3})$

While, if,

$x+\frac{p+2q}{3} = 0\implies x = -(\frac{p+2q}{3})$

Which are the required value of x.