Question

7. If 5x – 2y = 7 and xy = 2, find the value of 25x^2 – 4y^2.

the answer is coming
$\sqrt{16}$
can anyone explain I'll mark brainliest for 1st answer​

Answer 1

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Answer 2

xy = 2

5x - 2y = 7 ... (i)

squaring both the sides, we get

25x² - 20xy + 4y² = 49

25x² - 20(2) + 4y² = 49 (given xy = 2)

25x² + 4y² - 40 = 49

25x² + 4y² = 89

(5x + 2y)² - 20xy = 89

(5x + 2y)² - 20(2) = 89

(5x + 2y)² - 40 = 89

(5x + 2y)² = 129

taking square roots on both sides

5x + 2y = √129 ... (ii)

now,

25x² - 4y²

= (5x)² - (2y)²

= (5x + 2y)(5x - 2y)

= (√129)(7) ... (from i and ii)

= 7√129

Hence, 25x² - 4y² = 7√129