Question

Express 9x²-42xy+49y² as a perfect square and hence find it's value when 3x-7y=5​

Answer 1

Answer:

(3x-7y)²

25

Step-by-step explanation:

9x² - 42xy + 49y²

using a² -2ab + b² = (a-b)²

here,

a² = 9x² ⇒ a = 3x (using square root both side)

b² = 49y² ⇒ b = 7y (using square root both side)

2ab = 42xy ⇒ 2ab = 2 × 3x × 7y

∴ 9x²-42xy+49y² = (3x)² - 2×3x×7y + (7y)² = (3x-7y)²

∵ 3x-7y = 5

substituting 3x-7y with 5 in (3x-7y)²

⇒5² = 25