Question

solve solve solve solve solve

Answer 1

EXPLANATION.

(1) = √(2x + 9) + x = 13.

As we know that,

We can write equation as,

⇒ √2x + 9 = 13 - x.

Squaring on both sides of equation, we get.

⇒ (√2x + 9)² = (13 - x)².

⇒ 2x + 9 = (13 - x)².

As we know that,

Formula of :

⇒ (x - y)² = x² + y² - 2xy.

Using this formula in equation, we get.

⇒ 2x + 9 = 169 + x² - 26x.

⇒ x² - 26x - 2x + 169 - 9 = 0.

⇒ x² - 28x + 160 = 0.

Factorizes the equation into middle term splits, we get.

⇒ x² - 20x - 8x + 160 = 0.

⇒ x(x - 20) - 8(x - 20) = 0.

⇒ (x - 8)(x - 20) = 0.

⇒ x = 8  and  x = 20.

(2) = √(y² - y + 2) + y = 1.

As we know that,

We can write equation as,

⇒ √y² - y + 2 = 1 - y.

Squaring both the equation, we get.

⇒ (√y² - y + 2)² = (1 - y)².

⇒ y² - y + 2 = (1 - y)².

As we know that,

Formula of :

⇒ (x - y)² = x² + y² - 2xy.

Using this formula in equation, we get.

⇒ y² - y + 2 = 1 + y² - 2y.

⇒ y² - y + 2 - 1 - y² + 2y = 0.

⇒ - y + 2y + 2 - 1 = 0.

⇒ y + 1 = 0.

⇒ y = -1.

                                                                                                                         

MORE INFORMATION.

Nature of the factors of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.  

Answer 2

Solution

(1) = √(2x + 9) + x = 13.

As we know that,

We can write equation as,

⇒ √2x + 9 = 13 - x.

Squaring on both sides of equation, we get.

⇒ (√2x + 9)² = (13 - x)².

⇒ 2x + 9 = (13 - x)².

As we know that,

Formula of :

⇒ (x - y)² = x² + y² - 2xy.

Using this formula in equation, we get.

⇒ 2x + 9 = 169 + x² - 26x.

⇒ x² - 26x - 2x + 169 - 9 = 0.

⇒ x² - 28x + 160 = 0.

Factorizes the equation into middle term splits, we get.

⇒ x² - 20x - 8x + 160 = 0.

⇒ x(x - 20) - 8(x - 20) = 0.

⇒ (x - 8)(x - 20) = 0.

⇒ x = 8  and  x = 20.

(2) = √(y² - y + 2) + y = 1.

As we know that,

We can write equation as,

⇒ √y² - y + 2 = 1 - y.

Squaring both the equation, we get.

⇒ (√y² - y + 2)² = (1 - y)².

⇒ y² - y + 2 = (1 - y)².

As we know that,

Formula of :

⇒ (x - y)² = x² + y² - 2xy.

Using this formula in equation, we get.

⇒ y² - y + 2 = 1 + y² - 2y.

⇒ y² - y + 2 - 1 - y² + 2y = 0.

⇒ - y + 2y + 2 - 1 = 0.

⇒ y + 1 = 0.

⇒ y = -1.

                                                                                                                         

MORE INFORMATION.

Nature of the factors of the quadratic expression.

(1) = Real and different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.