Question

If a+b=4, ab=6, find the value of i) a-b ii) a²-b²

Answer 1

$(a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab$

$16 - 2ab = a {}^{2} + b {}^{2}$

$16 - 2 \times 6 = a {}^{2} + b {}^{2}$

$a {}^{2} + b {}^{2} = 4$

Now

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

$put \: value \: of \: a {}^{2} + b {}^{2}$

$(a - b) {}^{2} = 4 - 2 \times 6$

$(a - b) {}^{2} = - 8$

$a - b = 2 \sqrt{2} i$

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

$a {}^{2} - b {}^{2} = (4)(2 \sqrt{2}i)$

$a {}^{2} - b {}^{2} = 8 \sqrt{2} i$


Thanks