Question

c) If x2+ y2 = 25 and x y = 12, find the value of
2 (x + y)2 + 3(x - y)2​

Answer 1

$\huge{\underline{\underline{\red{\bf{Given:}}}}}$

• x²+y²=25.
• xy = 12

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$\huge{\underline{\underline{\red{\bf{To\: Find:}}}}}$

• The value of 2(x + y)²+3(x - y)²

$\rule{200}4$

$\huge{\underline{\underline{\red{\bf{Identities\:Used:}}}}}$

• (a + b)²= a²+b²+2ab.
• (a - b)²= a²+b²-2ab .

$\rule{200}4$

$\huge{\underline{\underline{\red{\bf{Answer:}}}}}$

Given that x² + y² = 25

⇒x ² + y² = 25.

⇒x² + y² + 2xy = 25 + 2xy .

⇒ (x + y)² = 25 + 2× 12.

⇒(x + y)² = 25 + 24 .

⇒(x + y)²= 49. ..................(i)

$\rule{200}2$

Again ,

⇒x ² + y² = 25.

⇒x² + y² -2xy = 25 -2xy .

⇒ (x - y)² = 25 - 2× 12.

⇒(x - y)² = 25 -24 .

⇒(x - y)² = 1. ......................(ii)

$\rule{200}2$

Now we have to find value of 2(x + y)²+3(x - y)².

On putting values from (i) and (ii) ,

⇒ 2(x + y)²+3(x - y)² = 2(49)+3(1)

⇒ 2(x + y)²+3(x - y)² = 2×49+ 3×1 .

⇒ 2(x + y)²+3(x - y)² = 98 + 3

⇒ 2(x + y)²+3(x - y)² = 111.

Hence the required value is 111.

Answer 2

Answer:

${} \huge \mathfrak \pink{answer}$

${x}^{2} + {y }^{2} = 25$

$so \: .by \: using \: {a+b}^{2} = {a}^{2} + {b}^{2} + 2ab$

${x + y}^{2} = 25+ 2 \times 12$

${x + y }^{2} = 25 + 24 = 49$

$so \: x + y = \sqrt{49}$

$so \: x + y = 7$

hope it helps u