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Solve x + 2 + y + 3 + {(x + 2)(y + 3)} = 39. (x + 2)^{2} + (y

Question

Solve $x + 2 + y + 3 + (x + 2) (y + 3) = 39$ .
$(x + 2)^{2} + (y + 3)^{2} + (x + 2) (y + 3) = 741$ .

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Solve

x + 2 + y + 3 + (x + 2) (y + 3) = 39

(x + 2)^{2} + (y + 3)^{2} + (x + 2) (y + 3) = 741

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Text solutionVerified

x + 2 + y + 3 + (x + 2) (y + 3) = 39

(x + 2)^{2} + (y + 3)^{2} + (x + 2) (y + 3) = 741

Let

x + 2 = p, y + 3 = q .

p + q + pq = 39 ⟶ I

p^{2} + q^{2} + pq = 741 ⟶ II

⟹ p + q - 39 = - pq

Squaring on both sides:-

⟹ p^{2} + q^{2} + 1521 + 2 pq - 78 p - 78 q = pq

⟹ p^{2} + q^{2} + pq = 78 p + 78 q - 1521 ⟶ III

Subtracting

II

from

III

78 p + 78 q - 1521 - 741 = 0

78 p + 78 q - 2262 = 0

p + q = 29 ⟶ I V

From

I

pq = 10

pq = 100 ⟶ V

p - q = (p + q)^{2} - 4 pq

= 841 - 400

= 441 = 21 ⟶ V I

Adding

I V

and

V I

2 p = 50

p = 25, q = 4

x + 2 = 25, y + 3 = 4

x = 23, y = 1

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