Question

if a + b = 7 and ab = 10 find the value of ( a^2 + b^2)​

Answer 1

Answer:

(a+b)^2=a^2+b^2+2ab

putting values

(7)^2=a^2+b^2+2*10

49=a^2+b^2+20

49-20=a^2+b^2

29=a^2+b^2

Answer 2

$\huge \fbox{ᴀɴsᴡᴇʀ}$

$\large \underline{ \underline{ \frak{ \color{red}ɢɪᴠᴇɴ::}}}$

$\mapsto \sf{a+b=7 \: and \: ab=10}$

$\large \underline{ \underline{ \frak{ \color{cyan}ᴛᴏ \: ғɪɴᴅ::}}}$

$\leadsto \sf{a² + b²}$

$\large \underline{ \underline{ \frak{ \color{indigo}ɪᴅᴇɴᴛɪᴛʏ \: ʀᴇϙᴜɪʀᴇᴅ::}}}$

$\rightarrow \sf{(a+b)²=a²+b²+2ab}$

$\large \underline{ \underline{ \frak{ \color{blue}ᴀᴄᴄᴏʀᴅɪɴɢ \: ᴛᴏ \: ϙᴜᴇsᴛɪᴏɴ::}}}$

$\dashrightarrow \sf{(a+b)²=a²+b²+2ab}$

$\dashrightarrow \sf{(7)²=a²+b²+2 \times 10}$

$\dashrightarrow \sf{49=a²+b²+20}$

$\dashrightarrow \sf{a²+b² = 49 - 20}$

$\dashrightarrow \sf{a²+b² =29}$

$\bf \underline{ʜᴇɴᴄᴇ,}$

$\implies \sf{Value \: of \: a²+b² \: is \: 29.}$