Question

the roots of the quadratic equation 1/a+b+X=1/a+1/b+1/X, a+b is not equal to 0 is
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Answer 1

Qᴜᴇsᴛɪᴏɴ :-

• Find the roots of the quadratic equation 1/(a+b+X) = (1/a) + (1/b) +(1/X) , where a+b is not equal to 0 ?

Sᴏʟᴜᴛɪᴏɴ :-

⟿ 1/(a+b+X) = (1/a) + (1/b) +(1/X)

⟿ 1/(a+b+X) - (1/x) = (1/a) + (1/b)

Taking LCM of Both sides,

⟿ {x - (a + b + x)}/{(a+b+x)x = (b + a)/ab

⟿ {x - a - b - x)}/{(a+b+x)x = (b + a)/ab

⟿ - (a + b) / {(a+b+x)x = (b + a)/ab

⟿ - 1/ {(a+b+x)x = 1/ab

⟿ - ab = (a + b + x)x

⟿ - ab = ax + bx + x²

⟿ x² + bx + ax + ab = 0

⟿ x² + ax + bx + ab = 0

⟿ x(x + a) + b(x + a) = 0

⟿ (x + a)(x + b) = 0

Putting Both Equal to Zero now, we get,

⟿ (x + a) = 0

⟿ x = (-a) (Ans).

and,

⟿ (x + b) = 0

⟿ x = (-b) (Ans.)

Hence, Roots of The Quadratic Equation are (-a) & (-b).

Answer 2

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