Solve the following equations by factorisation:
x(x + 1) +(x + 2)(x + 3) = 42
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Given,
⇒x(x+1)+(x+2)(x+3)=42⇒x2+x+x2+3x+2x+6=42⇒2x2+6x+6=42⇒2x2+6x+6−42=0⇒2x2+6x−36=0⇒2(x2+3x−18)=0⇒x2+3x−18=0⇒x2+6x−3x−18=0⇒x(x+6)−3(x+6)=0⇒(x−3)(x+6)=0⇒x−3=0 or x+6=0x=3 or x=−6\Rightarrow x(x + 1) + (x + 2)(x + 3) = 42 \\[1em] \Rightarrow x^2 + x + x^2 + 3x + 2x + 6 = 42 \\[1em] \Rightarrow 2x^2 + 6x + 6 = 42 \\[1em] \Rightarrow 2x^2 + 6x + 6 - 42 = 0 \\[1em] \Rightarrow 2x^2 + 6x - 36 = 0 \\[1em] \Rightarrow 2(x^2 + 3x - 18) = 0 \\[1em] \Rightarrow x^2 + 3x - 18 = 0 \\[1em] \Rightarrow x^2 + 6x - 3x - 18 = 0 \\[1em] \Rightarrow x(x + 6) - 3(x + 6) = 0 \\[1em] \Rightarrow (x - 3)(x + 6) = 0 \\[1em] \Rightarrow x - 3 = 0 \text{ or } x + 6 = 0 \\[1em] x = 3 \text{ or } x = -6⇒x(x+1)+(x+2)(x+3)=42⇒x2+x+x2+3x+2x+6=42⇒2x2+6x+6=42⇒2x2+6x+6−42=0⇒2x2+6x−36=0⇒2(x2+3x−18)=0⇒x2+3x−18=0⇒x2+6x−3x−18=0⇒x(x+6)−3(x+6)=0⇒(x−3)(x+6)=0⇒x−3=0 or x+6=0x=3 or x=−6
Hence, roots of given equation are 3 , -6.
Answered By
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x+15=x+3\sqrt{x + 15} = x + 3x+15=x+3
