If a + b = 5 and ab = 6, 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 = 5 and ab = 6 ⇒ (5) 2 = a 2 \+ 2 x 6 \+ b 2 ⇒ 25 = a 2 \+ 12 \+ b 2 ⇒ a 2 \+ b 2 = 25 \- 12 ⇒ a 2 \+ b 2 = 13 Hence, the value of (a 2 \+ b 2 ) is 13.

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Mathematics

If a + b = 5 and ab = 6, 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 = 5 and ab = 6

⇒ (5)² = a² + 2 x 6 + b²

⇒ 25 = a² + 12 + b²

⇒ a² + b² = 25 - 12

⇒ a² + b² = 13

Hence, the value of (a² + b²) is 13.

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Mathematics

If a + b = 5 and ab = 6, find a² + b²

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