Question

If a + b = 7 and ab = 6, find :
i)a-b
ii) a^2 - b^2​

Answer 1

Answer:

the answer Is given in the attachment

Answer 2

Answer:

$1. \: a - b \: = 5 \\ 2. \: {a}^{2} - {b}^{2} = 35$

Step-by-step explanation:

$a + b = 7 \\ ab = 6 \\ Since,(a + b) ^{2} = {a}^{2} + {b}^{2} + 2ab \\ = > {7}^{2} = {a}^{2} + {b}^{2} + 2 \times 6 = > 49 = {a}^{2} + {b}^{2} + 12 \\ = > 49 - 12 = {a}^{2} + {b}^{2} \\ = > {a}^{2} + {b}^{2} = 37$

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$Since, \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ = {(a - b)}^{2} = 37 - 2 \times 6 \\ = > {(a - b)}^{2} = 37 - 12 \\ = > {(a - b)}^{2} = 25 \\ = > a - b = \sqrt{25} \\ = > a - b = 5$

$Since,(a + b)(a - b) = {a}^{2} - {b}^{2} \\ = > {a}^{2} - {b}^{2} = 7 \times 5 \\ = > {a}^{2} - {b}^{2} = 35$