Question

if X, Y and Z are in continued proportion then ( X + Y + Z) (X-Y+ Z )=​

Answer 1

$= > (x + y + z)(x - y + z) \\ \\ \: \: \: \: \: take \: \: x + z = a \: and \: b = y \\ \\ = > (x + z + y)(x + z - y) \\ \\ = > (a + b)(a - b) \\ \\ = > {a}^{2} - {b}^{2} \\ \\ = > {(x + z)}^{2} - {y}^{2} \: \: \: \: \: \: \: \because \: a = x + z \ and \: \: b = y \\ \\ = > {x }^{2} + {z}^{2} + 2xz - {y}^{2} \\ \\ = > {x}^{2} - {y}^{2} + {z}^{2} + 2xz \\ \\ hope \: it \: helps \: you$

Answer 2

(x+y+z) (x-y+z)

=》(x+z)^2 -y^2.......[From the formula of (a+b)(a-b) =a^2-b^2]

=》x^2+z^2+2xz-y^2

=》X^2 -y^2+z^+2xz

Answer ✔