Question

2. If (a - b) = 5 and ab = 14 ; find the value of a^2 + b^2.
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Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

(a-b) =5

a-b =5

a=5+b....1

ab = 14.....2

Using equation 1 in equation 2

ab = 14

(5+b) b = 14

${b}^{2} + 5b = 14 \\ {b}^{2} + 5b - 14 = 0 \\ by \: fractoristion \: method \\ {b}^{2} + 7b - 2b - 14 = 0 \\ ( {b}^{2} + 7b)( - 2b - 14) = 0 \\ b(b + 7) - 2(b + 7) = 0 \\( b + 7)(b - 2) = 0 \\ ( b + 7) = 0 \: \: or \: \: (b - 2) = 0 \\ b = - 7 \: \: or \: \: b = 2$

From equation 1

a=5+b

a = 5 + (-7) or a = 5+2

a = -2. or a= 7

$for \: a = - 2 \: \: \: \: \: b \: = - 7 \\ {a}^{2} + {b}^{2} = {( - 2})^{2} + {( - 7})^{2} \\ = 4 + 49 = 53$

$for \: a = 7 \: \: \: \: \: \: \: \: b = 2 \\ {a}^{2} + {b}^{2} = {7}^{2} + {2}^{2} = 49 + 4 = 53$

$for \: a = 7 \: \: \: \: \: \: \: \: \: \: b = - 7 \\ {a}^{2} + {b}^{2} = {7}^{2} + {( - 7)}^{2} = 49 + 49 = 98$

$for \: a = - 2 \: \: \: \: \: \: \: \: \: b = 2 \\ {a}^{2} + {b}^{2} = { - 2}^{2} + {2}^{2} = 4 + 4 = 8$

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