Question

if a+b+c=0,then a. a+b.b+2a.b-c. c​

Answer 1

★ Question -

If ,

a + b + c = 0

Then ,

a.a + b.b + 2a.b - c.c = ?

★ Solution :

➜ Given -

• a + b + c = 0

➜ To Find -

• a.a + b.b + 2a.b - c.c

➜ Answer -

As ,

$\rm \: a + b + c = 0$

so ,

$\rm \implies \: a + b = - c \: ....(i)$

Now ,

$\rm \mapsto \: a.a \: + b.b + 2a.b - c.c$

$\mapsto \rm \: {a}^{2} + {b}^{2} + 2ab - {c}^{2}$

$\mapsto \rm \: {(a + b)}^{2} - {c}^{2}$

From eq(i) ,

$\mapsto \rm \: ( - c)^{2} - {c}^{2}$

$\mapsto \rm \: {c}^{2} - {c}^{2}$

$\mapsto \: 0$

So ,

$\longrightarrow \boxed{ \rm a.a + b.b + 2a.b - c.c = 0}$

✧ Formula Used -

• a²+b²+2ab = (a+b)²
• a² - b² = (a+b)(a-b)