Factorise :
x2+14x2+1−7x−72xx^2 + \dfrac{1}{4x^2} + 1 - 7x - \dfrac{7}{2x}x2+4x21+1−7x−2x7
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Given,
=x2+14x2+1−7x−72x=x2+(12x)2+1−7(x+12x)=x2+(12x)2+2×x×12x−7(x+12x)=(x+12x)2−7(x+12x)=(x+12x)(x+12x−7).\phantom{=} x^2 + \dfrac{1}{4x^2} + 1 - 7x - \dfrac{7}{2x} \\[1em] = x^2 + \Big(\dfrac{1}{2x}\Big)^2 + 1 - 7\Big(x + \dfrac{1}{2x}\Big) \\[1em] = x^2 + \Big(\dfrac{1}{2x}\Big)^2 + 2 \times x \times \dfrac{1}{2x} - 7\Big(x + \dfrac{1}{2x}\Big) \\[1em] = \Big(x + \dfrac{1}{2x}\Big)^2 - 7\Big(x + \dfrac{1}{2x}\Big) \\[1em] = \Big(x + \dfrac{1}{2x}\Big)\Big(x + \dfrac{1}{2x} - 7\Big).=x2+4x21+1−7x−2x7=x2+(2x1)2+1−7(x+2x1)=x2+(2x1)2+2×x×2x1−7(x+2x1)=(x+2x1)2−7(x+2x1)=(x+2x1)(x+2x1−7).
Hence, x2+14x2+1−7x−72x=(x+12x)(x+12x−7).x^2 + \dfrac{1}{4x^2} + 1 - 7x - \dfrac{7}{2x} = \Big(x + \dfrac{1}{2x}\Big)\Big(x + \dfrac{1}{2x} - 7\Big).x2+4x21+1−7x−2x7=(x+2x1)(x+2x1−7).
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