Solve the following quadratic equation:

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asked Feb 16 in Class X Maths by navnit40 (-4,671 points)

Solve the following quadratic equation:

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answered Feb 16 by priya12 (-12,484 points)

(i) 1/a + b + x = 1/a + 1/b + 1/x

⇒ 1/a + b + x – 1/x = 1/a + 1/b

⇒ x – a – b – x/x(a + b + x) = 1/a + 1/b

-(a + b)/x(a + b + x) = a + b/ab

⇒ x(a + b + x)(a + b)  =  -(a + b)ab

⇒ x(a +  b + x)(a + b) + ab(a + b) = 0

⇒ (a + b){x(a + b + x) + ab} = 0

⇒ a + b  or  x(a + b + x) + ab = 0

But  a + b ≠ 0

So  x(a + b + x) + ab = 0

⇒ x(a + b) + x2 + ab = 0

⇒ x2 + ax + bx + ab = 0

⇒ x(x + a) + b(x + a) = 0

⇒ (x + a)(x + b) = 0

⇒  x = - a  or  x = - b

(ii) 4x2 – 4ax + (a2 – b2) = 0

Where a, b ∈ R

⇒  4x2 – {2(a + b)x + 2(a – b)x} + a2 – b2 = 0

⇒ {4x2 – 2(a + b)x}  - {2(a – b)x – (a2 – b2)} = 0

⇒ 2x{2x – (a + b)} – (a – b) {2x – (a + b)} = 0

⇒ {2x – (a + b)} {2x  - (a – b)} = 0

⇒ 2x – (a + b) = 0

or    2x – (a – b) = 0

⇒  x = a + b/2   or   x = a – b/2

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