Question

If a + b = 6 and ab = 8, evaluate (1)
${a}^{2} + b {}^{2}$
(2) a-b.​

Answer 1

$\large\orange{\mid{\fbox{\sf{Given}}\mid}}$

a + b = 6 and ab = 8

for equation (1),

${\small{\boxed{\green{\bf{Given\:expression}}}}}$$= {a}^{2} + {b}^{2}$

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

$= {(6)}^{2} - 2 \times 8$

$= 36 - 16$

$= 20$

for equation (2),

${\blue{\sf\underline{we\:know,}}}$

$(a-b)²=(a+b)²-4ab$

$(a-b)²=(6)² - 4×8$

$(a-b)²= 36-32$

$(a-b)²=4$

$(a-b)=√4$

$a-b = 2$