Question

If 2a-b+c=0, then show that
4a² - b² +c²+
4ac=0​

Answer 1

$Given \: 2a - b + c = 0$

$\implies 2a + c = b$

/* On squaring both sides of the equation */

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

/* By algebraic identity */

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

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

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

/*Rearranging the terms , we get */

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

$Hence \: proved .$

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