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If (x - y)= 74 and 2x² + 2y² = 36, find the value of 5xy.​

Sagot :

Answer:

5xy = - 13645

Step-by-step explanation:

Note that

(x - y)² = x² + y² - 2xy

Given

2x² + 2y² = 36 ( divide through by 2 )

x² + y² = 18

Then

(x- y)² = 74² = 5746 ← expand left side

x² + y² - 2xy = 5746 ← substitute x² + y² = 18

18 - 2xy = 5746 ( subtract 18 from both sides )

- 2xy = 5458 ( divide both sides by - 2 )

xy = - 2729

Thus

5xy = 5 × - 2729 = - 13645

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