Question

help plz ....... .......​

Answer 1

GIVEN :–

$\\ \tt \implies{a}^{2}+{b}^{2} + {c}^{2} = 250$

$\\ \tt \implies ab + bc + ca = 3$

$\\ \tt \implies a+b+c=x$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

$\\ \tt \implies a+b+c=x$

• Now square on both sides –

$\\ \tt \implies (a+b+c)^{2} = {(x)}^{2}$

• We know that –

$\\ \: \: \large\bigstar \: \: {\boxed{ \bf (a+b+c)^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca)}}$

• So that –

$\\ \tt\implies {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) = {x}^{2}$

• Now put the values –

$\\ \tt\implies 250+ 2(3) = {x}^{2}$

$\\ \tt\implies {x}^{2} = 250+ 2(3)$

$\\ \tt\implies {x}^{2} = 250+6$

$\\ \tt\implies {x}^{2} = 256$

$\\ \tt\implies x= \sqrt{256}$

$\\ \large\implies{ \boxed{ \tt x= \pm16}}$

Answer 2

Solutions:

GIVEN :–

$\begin{gathered} \\ \tt \implies{a}^{2}+{b}^{2} + {c}^{2} = 250 \\ \end{gathered}$

$\begin{gathered} \\ \tt \implies ab + bc + ca = 3\\ \end{gathered}$

$\begin{gathered} \\ \tt \implies a+b+c=x\\ \end{gathered}$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

$\begin{gathered} \\ \tt \implies a+b+c=x\\ \end{gathered}$

• Now square on both sides –

$\begin{gathered} \\ \tt \implies (a+b+c)^{2} = {(x)}^{2} \\ \end{gathered}$

• We know that –

$\begin{gathered} \\ \: \: \large\bigstar \: \: {\boxed{ \bf (a+b+c)^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca)}}\\ \end{gathered}$

• So that –

$\begin{gathered} \\ \tt\implies {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) = {x}^{2} \\ \end{gathered}$

• Now put the values –

$\begin{gathered} \\ \tt\implies 250+ 2(3) = {x}^{2} \\ \end{gathered}$

$\begin{gathered} \\ \tt\implies {x}^{2} = 250+ 2(3)\\ \end{gathered}$

$\begin{gathered} \\ \tt\implies {x}^{2} = 250+6\\ \end{gathered}$

$\begin{gathered} \\ \tt\implies {x}^{2} = 256\\ \end{gathered}$

$\begin{gathered} \\ \tt\implies x= \sqrt{256}\\ \end{gathered}$