Question

if 2a-b+c=0 prove that 4a^2-b^2+c^2+4ac=0

plzzzz ansr this

Answer 1

Given,

The value of 2a-b+c = 0

To Prove,

The value of 4a²+b²+c²+4ac = 0

Solution,

Since we are given that

2a-b+c = 0

2a+c = b

Now, squaring both sides

(2a+c)² = b²

Using the identity (a+b) = a²+b²+2ab

So,

(4a²+c²+4ac) = b²

4a²+c²+4ac-b² = 0

4a²-b²+c²+4ac = 0

Hence proved that the value of 4a²-b²+c²+4ac = 0.

Answer 2

Given,

The value of 2a-b+c = 0

To Prove,

The value of 4a²+b²+c²+4ac = 0

Solution,

formal to be used=

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

Since we are given that

2a-b+c = 0

2a+c = b

Now, squaring both sides

${(2a + c)}^{2} = {b}^{2}$

$4 {a}^{2} + {c}^{2} + 4ac = {b}^{2}$

$4 {a}^{2} - {b}^{2} + {c}^{2} + 4ac = 0$

Hence proved ,

$4 {a}^{2} - {b}^{2} + {c}^{2} + 4ac$ =0