Question

Answer fastly for brainliest

Answer 1

Answer:

Option(2) - 8

Step-by-step explanation:

Given: x = (1/2 + √3)

On rationalizing, we get

⇒ (1/2 + √3) * (2 - √3)/(2 - √3)

⇒ (2 + √3)/(2)² - (√3)²

⇒ (2 + √3)/4 - 3

⇒ 2 + √3

So,

x = 2 + √3

⇒ x - 2 = √3

On Squaring both sides, we get

⇒ (x - 2)² = (√3)²

⇒ x² + 4 - 4x = 3

⇒ x² - 4x + 1 = 0

Now,

Given Expression is x³ - 2x² - 7x + 10

= x³ - 4x² + 2x² - 7x + 10

= x³ - 4x² + x - x + 2x² - 7x + 10

= x(x² - 4x + 1) + 2x² - 8x + 10

= x(0) + 2(x² - 4x + 5)

= 2(x² - 4x + 1 + 4)

= 2(4)

= 8

Hope it helps!

Answer 2

Substitute the specified value of x into the equation. We’ll split the terms to allow for easier computation.

x^3 = (1/2 - sqrt3)^3, which upon expanding and simplifying gives us 37/8 - 15/4*sqrt3

-2x^2 = -2(1/2 - sqrt3)^2, which upon expanding and simplifying gives us -13/2 + 2sqrt3

-7x = -7(1/2 -sqrt3), which upon expanding and simplifying gives us -7/2 + 7sqrt3

Combine all 3 terms and the constant term (10) together to obtain 37/8 + 21/4*sqrt3.