Question

If a + b = 9 and ab = 10, find the value of a2 + b2.​

Answer 1

$\huge\bold\star\underline\pink{AnsWer:}$

$a + b = 9 - - eq(1) \: \\ \\ ab = 10 - - eq(2) \\ \\ squaring \: on \: both \: sides \: in \: eq(1) \\ \\ = > (a + b) {}^{2} = 9 {}^{2} \\ \\ = > {a}^{2} + {b}^{2} + 2ab = 81 \\ \\ = > {a}^{2} + b {}^{2} + 2(10) = 81 \: \: (from \: eq(2)) \\ \\ = > {a}^{2} + {b}^{2} = 81 - 20 \\ \\ = > {a}^{2} + {b}^{2} = 61$

$\large\text{\therefore{a^2+b^2\:=\:61}}$

Answer 2

$\\ \large\mathfrak {\underline \purple{ \: \: \: \: \: \: \: \: \: concept - \: \: \: \: \: \: \: \: }} \\ \\ \\ \sf \: here \: in \: the \: query ,\: the \: question \: said \: that \\ \sf \: the \: value \: of \: \blue {a + b \: is \: 9 }\: and \: the \: value \: of \: \blue{ ab \: is \: 10} \\ \sf \: and \: we \: have \: to \: find \: the \: value \: of \: \red { {a}^{2} + {b}^{2} }. \\ \sf \: by \: applying \: the \: formula \: \bigstar\boxed{ \bf \: (a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab } \bigstar$

$\\ \large\mathfrak {\underline \purple{ \: \: \: \: \: \: \: \: solution \: \: \: \: \: \: \: \: }} \\ \\ \\ \sf➲(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ \sf ➲(9) {}^{2} = {a}^{2} + {b}^{2} + 2 \times 10 \\ \\ \sf➲81 = {a}^{2} + {b}^{2} + 20 \\ \\ \sf➲81 - 20 = {a}^{2} + {b}^{2} \\ \\ \sf➲61 = {a}^{2} + {b}^{2} \\ \\ \sf➲ {a}^{2} + {b}^{2} = { \boxed{\boxed { \tt \red6 \pink1}}}$

$\sf \therefore \: the \: value \: of \: {a}^{2} + {b}^{2} \: is \: \red{61}$

$\\ \bigstar{ \underline{ \underline \pink{ \sf★@iTzShInNy☆}}} \bigstar$