Question

If a + b = 7 and ab = 6, then find the value of a² + b²

Answer 1

Hey!!

Here is your answer

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${a}^{2} + {b}^{2} \: = (a + b)(a - b)$

Given,
$(a + b) = 7 \\ a = 7 - b$

Now, put the values
$(a + b)(a - b) = (7)((7 - b) - b)$

$(7)(7 - 2b)$

$49 - 14b$

$49 = 14b$

$b = \frac{49}{14}$

$b = 3.5 \\ Now, \: put\: the\: value\: of\: b\: into\: the\: above\: statement \: \\ \\ as \: a =7 - b \\ a = 7 - 3.5 \\ a = 3.5$

Now, we have both the values a and b, put it in the formula
$(a + b)(a - b) \\ = (7)(3.5 - 3.5) \\ = (7)(0) \\ = 0$

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Thanks!!

Answer 2

Heya!!

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{a}^{2} + {b}^{2} \: = (a + b)(a - b)

Given,

(a + b) = 7 \\ a = 7 - b

Now, put the values

(a + b)(a - b) = (7)((7 - b) - b)

(7)(7 - 2b)

49 - 14b

49 = 14b

b = \frac{49}{14}

b = 3.5 \\ Now, \: put\: the\: value\: of\: b\: into\: the\: above\: statement \: \\ \\ as \: a =7 - b \\ a = 7 - 3.5 \\ a = 3.5

Now, we have both the values a and b, put it in the formula

(a + b)(a - b) \\ = (7)(3.5 - 3.5) \\ = (7)(0) \\ = 0

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Thanka!!☺