Question

if
$2( {a}^{2} + {b}^{2} ) = ( {a + b)}^{2}$
then prove that a=b​

Answer 1

Question :

If 2(a² + b²) = (a + b)² , then Prove that a = b.

Solution :

⇒ 2 ( a² + b² ) = ( a + b )² [ Given ]

• (a + b)² = (a² + b² + 2ab)

⇒ 2a² + 2b² = a² + b² + 2ab

⇒ 2a² - a² + 2b² - b² - 2ab = 0

⇒ a² + b² - 2ab = 0

• (a² + b² - 2ab) = (a - b)²

⇒ ( a - b )² = 0

• Squaring Root Both Side

⇒ √ ( a - b )² = √ 0

⇒ ( a - b ) = 0

⇒ a = b

჻ Hence, Proved a = b.