Question

solve with quadratic equation please

Answer 1

EXPLANATION.

$\sf \implies \sqrt{\dfrac{x}{x + 1} } \ + \ \sqrt{\dfrac{x + 1}{x} } = \dfrac{25}{12}$

As we know that,

$\sf \implies \sqrt{\dfrac{x}{x + 1} } = y$

Equations can be written as,

⇒ y + 1/y = 25/12.

⇒ y² + 1/y = 25/12.

⇒ 12(y² + 1) = 25y.

⇒ 12y² + 12 = 25y.

⇒ 12y² - 25y + 12 = 0.

Factorizes the equation into middle term splits, we get.

⇒ 12y² - 16y - 9y + 12 = 0.

⇒ 4y(3y - 4) - 3(3y - 4) = 0.

⇒ (4y - 3)(3y - 4) = 0.

⇒ y = 3/4  and  y = 4/3.

As we know that,

⇒ √x/x + 1 = y.

Put the value of y = 3/4 in equation, we get.

⇒ √x/x + 1 = 3/4.

Squaring on both sides of the equation, we get.

⇒ (√x/x + 1)² = (3/4)².

⇒ x/x + 1 = 9/16.

⇒ 16x = 9(x + 1).

⇒ 16x = 9x + 9.

⇒ 16x - 9x = 9.

⇒ 7x = 9.

⇒ x = 9/7.

Put the value of y = 4/3 in equation, we get.

⇒ √x/x + 1 = 4/3.

Squaring on both sides of the equation, we get.

⇒ (√x/x + 1)² = (4/3)².

⇒ x/x + 1 = 16/9.

⇒ 9x = 16(x + 1).

⇒ 9x = 16x + 16.

⇒ 9x - 16x = 16.

⇒ - 7x = 16.

⇒ x = - 16/7.

                                                                                                                         

MORE INFORMATION.

Conjugate roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

Answer:

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