Question

The sum of two quantities is (4a²-3ab+b²) . If one of them is 7a²+2ab-b², find the other.

Answer 1

Answer :-

The other quantity is -3a²-5ab+2b².

Step-by-step explanation:

To Find :-

• The other quantity.

★ Solution

Given that,

• The sum of two quantities = 4a²-3ab+b²
• One of the quantity = 7a²+2ab-b²

∴ According the question,

⇒ Other quantity + (7a²+2ab-b²) = (4a²-3ab+b²)

⇒ (4a²-3ab+b²) - (7a²+2ab-b²)

⇒ 4a² - 3ab + b² + -1(7a² + 2ab - b²)

⇒ 4a² - 3ab + b² + -1(7a²) + -1(2ab) + -1(-b²)

⇒ 4a² - 3ab + b² + -7a² - 2ab + b²

⇒ 4a² - 3ab + b² - 7a² - 2ab + b²

⇒ 4a² - 7a² - 3ab - 2ab + b² + b²

⇒ -3a² - 3ab - 2ab + b² + b²

⇒ -3a² - 5ab + b² + b²

⇒ -3a² - 5ab + 2b²

The other quantity is -3a² - 5ab + 2b².

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Now,

V E R I F I C A T I O N :-

(-3a²-5ab+2b²) + (7a²+2ab-b²) = (4a²-3ab+b²)

By simplifying the L.H.S :-

⇒ (-3a²-5ab+2b²) + (7a²+2ab-b²)

⇒ -3a² - 5ab + 2b² + 7a² + 2ab - b²

⇒ -3a² + 7a² - 5ab + 2ab + 2b² - b²

⇒ 4a² - 5ab + 2ab + 2b² - b²

⇒ 4a² - 3ab + 2b² - b²

⇒ 4a² - 3ab - b²

Now, L.H.S = R.H.S = 4a² - 3ab - b²

Hence, Verified!