Question

if a+b =7and ab =10, find the value of (a-b).
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Answer 1

Answer:

${(a + b)}^{2} = {a}^{2} + {b}^{2} +2ab \\ {7}^{2} = {a}^{2} + {b}^{2} + 2 \times 10 \\ 49 = {a }^{2} + {b}^{2} + 20 \\ 49 - 20 = {a}^{2} + {b }^{2} \\ 29 = {a}^{2} + {b}^{2} \\ \\ {(a - b)}^{2} = {a }^{2} + {b}^{2} - 2ab \\ {(a - b)}^{2} = 29 - 2 \times 10 \\ {(a - b)}^{2} = 29 - 20 \\ {(a - b)}^{2} = 9 \\ a - b = \sqrt{9} \\ a - b = + 3 \: or - 3$