Question

Given that
$a + b = 10$
and
$a {}^{2} - b {}^{2} = 40$
, find the value of
$a - b$
​

Answer 1

Step-by-step explanation:

Given:-

a+b=10

a^2-b^2=40

To find:-

Find the value of a-b?

Solution:-

Given that:

a+b=10----(1)

a^2-b^2=40

=>(a+b)(a-b)=40

=>10(a-b)=40 (from(1))

=>a-b=40/10

Therefore,a-b=4

Answer:-

The value of a-b=4

Used formula:-

• (a+b)(a-b)=a^2-b^2

Answer 2

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{a + b = 10} \\ &\sf{ {a}^{2} - {b}^{2} = 40 } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\sf{value \: of \: a - b}  \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  Identity \: used :-  \begin{cases} &\tt{ {x}^{2} - {y}^{2} = (x + y)(x - y) }  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

$\begin{gathered}\tt\red{According \: to \: statement}\end{gathered}$

$\tt \:  ⟼ \: {a}^{2} - {b}^{2} = 40$

$\tt \:  : \: ⟼ (a + b)(a - b) = 40$

$\tt \:  : \: ⟼ 10 \times (a - b) = 40$

$\tt \:  : \: ⟼ a - b \: = \dfrac{ \cancel{40}}{ \cancel{10}} \: 4$

$\bf\implies \:a \: - \: b \: = 4$