Question

If x+✓y=7 and ✓x+y=11 then find x and y
BUT WITHOUT HIT AND TRIAL METHOD


I WILL MARK HIM BRAINLIEST

Answer 1

Answer:

x = 4, y = 9

Step-by-step explanation:

We have,

(i) x + √y = 7

(ii) √x + y = 11

Equation (i) can be written as,

⇒ √y = 7 - x

On squaring both sides, we get

⇒ y = (7 - x)²    ------- (iii)

Now,

Let √x = t, then x = t².     --------- (*)

Equation (4) can be written as,

⇒ t + (7 - x)² = 11

⇒ t + (7 - t²)² = 11

⇒ t + 49 + t⁴ - 14t² = 11

⇒ t⁴ - 14t² + t + 38 = 0

⇒ t⁴ - 2t³ + 2t³ - 4t² - 10t² + 20t - 19t + 38 = 0

⇒ t³(t - 2) + 2t²(t - 2) - 10t(t - 2) - 19(t - 2) = 0

⇒ (t - 2)(t³ + 2t² - 10t - 19) = 0

⇒ t - 2 = 0, t³ + 2t² - 10t - 19 = 0{Neglect}

⇒ t = 2.

From (*), we get

⇒ x = t²

⇒ x = 4.

Substitute x = 4 in (ii), we get

⇒ √x + y = 11

⇒ √4 + y = 11

⇒ 2 + y = 11

⇒ y = 9

Therefore, the values are x = 4 and y = 9.

Hope it helps!

Answer 2

√x+y=7x+√y=11√x=7-y√y=11-xthe square root of a number is always the positive square roottherefore y can't be greater than 7 and x can't be greater than 11look at the perfect squares 1, 4, 9, 16assuming x and y are perfect squares and a little trial and error...x=9 and y=4