Question

The roots of the quadratic equation `1/("a" + "b" + "x") = 1/"a" + 1/"b" + 1/"x"`, a + b ≠ 0 is:

पर्याय

• a, b

• −a, b

• a, −b

• −a, −b

Answer 1

−a, −b

Explanation:

We have `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")) = ("a" + "b")/"ab"`

⇒ `(-("a" + "b"))/("x"("a" + "b" + "x")) = ("a" + "b")/"ab"`

⇒ ax + bx + x² = –ab

⇒ x² + ax + bx + ab = 0

⇒ x(x + a) + b(x + a) = 

⇒ (x + a) (x + b) = 0

∴ x = –a, x = –b