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Mathematics

Solve the following equation by factorisation:

3(x - 2)2 = 147

Quadratic Equations

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Answer

Given,

3(x2)2=1473(x24x+4)=1473x212x+12=1473x212x+12147=0 (Writing as ax2+bx+c=0)3x212x135=03x212x1353=03 (Dividing the complete equation by 3) x24x45=0x29x+5x45=0x(x9)+5(x9)=0(x9)(x+5)=0 (Factorising left side) x9=0 or x+5=0 (Zero-product rule) x=9 or x=5.3(x-2)^2 = 147 \\[1em] \Rightarrow 3( x^2 - 4x + 4) = 147 \\[1em] \Rightarrow 3x^2 - 12x + 12 = 147 \\[1em] \Rightarrow 3x^2 - 12x + 12 - 147 = 0 \text{ (Writing as } ax^2 + bx + c = 0) \\[1em] \Rightarrow 3x^2 - 12x - 135 = 0 \\[1em] \Rightarrow \dfrac{3x^2 - 12x - 135 }{3} = \dfrac{0}{3} \\[1em] \text{ (Dividing the complete equation by 3) } \\[1em] \Rightarrow x^2 - 4x - 45 = 0 \\[1em] \Rightarrow x^2 - 9x + 5x - 45 = 0 \\[1em] \Rightarrow x(x - 9) + 5(x - 9) = 0 \\[1em] \Rightarrow (x - 9)(x + 5) = 0 \text{ (Factorising left side) }\\[1em] \Rightarrow x - 9 = 0 \text{ or } x + 5 = 0 \text{ (Zero-product rule) } \\[1em] \Rightarrow x = 9 \text { or } x = -5.

Hence, the roots of given equation are 9, -5.

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