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प्रश्न
Solve the following quadratic equation:
`(1)/(a + b + x) = (1)/a + (1)/b + (1)/x, a + b ≠ 0`
उत्तर
`(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.
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