Question

Please solve the Question Which is in the Picture.

Answer 1

Answer:

x = 3

Step-by-step explanation:

Given Equation is √x + 1 + √2x - 5 = 3.

⇒ √x + 1 = 3 - √2x - 5

On Squaring both sides, we get

⇒ (√x + 1)² = (3 - √2x - 5)²

⇒ x + 1 = 9 - 6√2x - 5 + (2x - 5)

⇒ x + 1 = 9 - 6√2x - 5 + 2x - 5

⇒ x + 1 = 4 - 6√2x - 5

⇒ x - 3 = -6√2x - 5.

On squaring both sides, we get

⇒ (x - 3)² = (-6√2x - 5)²

⇒ x² + 9 - 6x = 36(2x - 5)

⇒ x² + 9 - 6x = 72x - 180

⇒ x² - 66x + 189 = 0

⇒ x² - 63x - 3 + 189 = 0

⇒ x(x - 63) - 3(x - 63) = 0

⇒ (x - 3)(x - 63) = 0

⇒ x = 3. {x = 63 doesn't satisfy the condition}

⇒ x = 3

Hope it helps!

Answer 2

Step-by-step explanation:

√x + 1 + √2x - 5 = 3.

√x + 1 = 3 - √2x - 5

(√x + 1)² = (3 - √2x - 5)²

x + 1 = 9 - 6√2x - 5 + (2x - 5)

x + 1 = 9 - 6√2x - 5 + 2x - 5

x + 1 = 4 - 6√2x - 5

x - 3 = -6√2x - 5.

(x - 3)² = (-6√2x - 5)²

x² + 9 - 6x = 36(2x - 5)

x² + 9 - 6x = 72x - 180

x² - 66x + 189 = 0

x² - 63x - 3 + 189 = 0

x(x - 63) - 3(x - 63) = 0

(x - 3)(x - 63) = 0

x = 3