Question

Answer these three please!!

Answer 1

10. x = 3 ± 2√6

11. x = 4 ± √6

12.
`x = (- 7 + √(109))/(10)` and
`x = (- 7 - √(109))/(10)`

Explanation:

10. Given the quadratic equation (x - 3)² + 14 = 38

We have to solve it by square root.

Now, (x - 3)² + 14 = 38

⇒ (x - 3)² = 38 - 14 = 24

⇒ (x - 3)² = (2√6)²

Now, square rooting both sides we get,

(x - 3) = ± 2√6

⇒ x = 3 ± 2√6 (Answer)

11. Given the quadratic equation x² - 8x + 10 = 0

We have to solve it by completing the square.

Now, x² - 8x + 10 = 0

⇒ x² - 2(4)(x) + 4² = 4² - 10

⇒ (x - 4)² = (√6)²

Now, square rooting both sides we get,

x - 4 = ± √6

⇒ x = 4 ± √6 (Answer)

12. Given the quadratic equation 5x² + 7x - 3 = 0

We have to solve it by quadratic formula.

Hence,

`x = \frac{- 7 + \sqrt{7^(2) - 4 (5)(- 3)}}{2(5)}` and
`x = \frac{- 7 - \sqrt{7^(2) - 4 (5)(- 3)}}{2(5)}`

⇒
`x = (- 7 + √(109))/(10)` and
`x = (- 7 - √(109))/(10)` (Answer)