Question

Find the roots of the equation (x² + 3x)² – (x² + 3x) –6 = 0. and tell why we should take x²+3x as y​

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• An equation
• (x² + 3x)² – (x² + 3x) –6 = 0.

${\sf{\green{\underline{\large{To\:find}}}}}$

• Roots of the equation

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Let x²+3x as y

Reasons

• Simplify by the equation
• easily find the roots.

New equation

(x² + 3x)² – (x² + 3x) –6 = 0.

=>y²-y-6=0

• Spilt the middle term in such a way that the product will be 6 and sum will be-1

=>y²-3y+2y-6=0

=>y(y-3)+2(y-3)=0

=>(y-3) (y+2)=0

=>y=3,-2

Taking y=3

X²+3x=-2

=>x²+3x+2

=>x²+2x+x+2

=>x(x+2)+1(x+2)

=>(x+1)(x+2)

=>x=-1,-2.

Hence roots if equation be -1 and -2