Question

If 3x - 7y= 10 and xy=-1 then the value 9x2+49y2 is

Answer 1

Answer:

$\large{\underline{\boxed{\sf 9x^2 + 49y^2 = 58}}}$

Explanation:

Given that ;

• 3x - 7y = 10
• xy = - 1

To find:

9x² + 49y²

Solution:

3x - 7y = 10

On squaring both sides -

⇒ (3x - 7y)² = (10)²

⇒ (3x)² + (7y)² - 2 * 3x * 7y = 100

⇒ 9x² + 49y² - 42 * xy = 100

⇒ 9x² + 49y² - 42 (-1) = 100

⇒ 9x² + 49y² + 42 = 100

⇒ 9x² + 49y² = 100 - 42

⇒ 9x² + 49y² = 58

Hence, the answer is 58.

$\rule{300}{2}$

$\large{\underline{\underline{\mathfrak{\heartsuit \: Algebraic \: Identities : \: \heartsuit}}}}$

• (a - b)³ = a³ - b³ - 3ab (a - b)
• (a + b)³ = a³ + b³ + 3ab (a + b)
• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (x + a)(x + b) = x² + x(a + b) + ab

Answer 2

Answer:

Explanation:

Given :-

3x - 7y = 10

xy = - 1

To Find :-

9x² + 49y² = ??

Formula to be used :-

Squaring both sides.

Solution :-

Squaring both sides, we get

(3x -7y)² = 100

⇒ 9x² + 49y² - 42xy = 100

⇒ 9x² + 49y² - 42 (-1) = 100

⇒ 9x² + 49y² + 42 = 100

⇒ 9x² + 49y² = 100 - 42

⇒ 9x² + 49y² = 58

Hence, the value of 9x² + 49y² is 58.