If a - b = 6 and ab = 16, find a^2 + b^2

Using the formula, [∵(x \- y) 2 = x 2 \- 2xy \+ y 2 ] So, (a \- b) 2 = a 2 \- 2ab \+ b 2 Putting the value, a \- b = 6 and ab = 16 ⇒ (6) 2 = a 2 \- 2 x 16 \+ b 2 ⇒ 36 = a 2 \- 32 \+ b 2 ⇒ a 2 \+ b 2 = 36 \+ 32 ⇒ a 2 \+ b 2 = 68 Hence, the value of (a 2 \+ b 2 ) is 68.

Mathematics

If a - b = 6 and ab = 16, find a² + b²

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Answer

Using the formula,

[∵(x - y)² = x² - 2xy + y²]

So,

(a - b)² = a² - 2ab + b²

Putting the value, a - b = 6 and ab = 16

⇒ (6)² = a² - 2 x 16 + b²

⇒ 36 = a² - 32 + b²

⇒ a² + b² = 36 + 32

⇒ a² + b² = 68

Hence, the value of (a² + b²) is 68.

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Mathematics

If a - b = 6 and ab = 16, find a² + b²

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