Question

solve this question please

Answer 1

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Answer 2

Answer:

1]. 4x² + 9y² = 40

2]. 9x² + 49y² = 58

Step-by-step explanation:

1]. Given:

2x + 3y = 8

xy = 2

To find : 4x² + 9y²

Apply Squaring L.H.S side

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

(2x + 3y)² = 4x² + 9y² + 12(xy)

Now , put in the known values

(8)² = 4x² + 9y² +12(2)

64 - 24 = 4x² + 9y²

4x² + 9y² = 40

2]. Given

3x - 7y = 10

xy = -1

To find : 9x² + 49y²

Apply Squaring L.H.S side

(3x - 7y )² = (3x)² + (7y)² - 2(3x)(7y)

(3x - 7y )² = 9x² + 49y² - 42(xy)

Now , put in the known values

(10)² = 9x² + 49y² - (-42)

100 = 9x² + 49y² + 42

100 - 42 = 9x² + 49y²

9x² + 49y²= 58

$\rule{200}{1}$

$\boxed{\underline{\bold{\mathsf{Identities \: Used}}}}$:—

★ (a - b)² = a² + b² - 2ab

★ (a + b)² = a² + b² + 2ab