Question

18. Given: Two positive integers such that: X - Y = 3 & X2 + Y2 = 36 Find X + Y?​

Answer 1

Answer:

X = 10.5

Y = 7.5

Step-by-step explanation:

X - Y = 3

X - Y = 3 10.5 - 7.5 = 3

X - Y = 3 10.5 - 7.5 = 3 X2 + Y2 = 36

X - Y = 3 10.5 - 7.5 = 3 X2 + Y2 = 362(10.5) + 2(7.5)

X - Y = 3 10.5 - 7.5 = 3 X2 + Y2 = 362(10.5) + 2(7.5)21 + 15

X - Y = 3 10.5 - 7.5 = 3 X2 + Y2 = 362(10.5) + 2(7.5)21 + 1536

hence proved

Answer 2

X + Y = 9

Given:

Two positive integers such that: X - Y = 3 & X2 + Y2 = 36.

To Find:

X + Y = ?​

Solution:

We are given that X - Y = 3 and X^2 + Y^2 = 45.

Squaring the first equation, we get:

(X - Y)^2 = 3^2

X^2 - 2XY + Y^2 = 9

Adding this equation to the second equation, we get:

2X^2 + 2Y^2 - 2XY = 54

But we also know that:

(X + Y)^2 = X^2 + 2XY + Y^2

Substituting X^2 + Y^2 = 45 and simplifying, we get:

(X + Y)^2 = 45 + 2XY

Substituting 2XY = 2X(X - Y) from the first equation, we get:

(X + Y)^2 = 45 + 2X(X - Y) = 45 + 2X(3) = 6(X + 5)

Taking the square root of both sides, we get:

X + Y = √(6(X + 5))

Substituting X + Y = 3 + Y, we get:

3 + Y = √(6(X + 5))

Squaring both sides and simplifying, we get:

9 + 6Y + Y^2 = 6X + 30

Substituting X - Y = 3, we get:

9 + 6Y + Y^2 = 6(Y + 3) + 30

Simplifying and solving for Y, we get:

Y = 3

Substituting Y = 3 in X - Y = 3, we get:

X = 6

Therefore, X + Y = 6 + 3 = 9. Answer: 9.

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