Question

If a^1/2 + b^1/2 - c^1/2 = 0, then the value of
(a + b-c)^2 is​

Answer 1

Answer:

√a+√b-√c=0

or, √a+√b=√c

Squaring both sides,

(√a)²+2√a√b+(√b)²=(√c)²

or, a+b+2√ab=c

or, a+b-c=-2√ab

Again squaring both sides,

(a+b-c)²=(-2√ab)²

or, (a+b-c)²=4ab

∴, The answer is c)4ab

Step-by-step explanation:

hope my answer help you

Answer 2

Given :-

• $\sf \;a^{\frac{1}{2}} + b^{\frac{1}{2}} - c^{\frac{1}{2}} = 0$

To Find :-

• Value of $\mathsf{(a + b - c)^2 }$

Solution :-

We are given :-

$\mathsf\pink{{\: \: \: \: \: \: \: \:\;a^{\frac{1}{2}} + b^{\frac{1}{2}} - c^{\frac{1}{2}} = 0}}$

$\mathsf{\: \: \: \: \: \: \: \::\implies a^{\frac{1}{2}} + b^{\frac{1}{2}} = c^{\frac{1}{2}}}$

⠀⠀⠀⠀⠀$\small\underline{\pmb{\sf Squaring \: on \: both \: sides:-}}$

$\implies \mathsf{\left(a^{\frac{1}{2}} + b^{\frac{1}{2}}\right)^2 = \left(c^{\frac{1}{2}}\right)^2}$

• Here,left side expression is in form of Identity : (a+ b)² We know that (a + b )² = a² + b² + 2ab.

$\: \: \: \: \: \: \: \::\implies \mathsf{\left(a^{\frac{1}{2}}\right)^2 + \left(b^{\frac{1}{2}}\right)^2 + 2\left(a^{\frac{1}{2}}\right)\left(b^{\frac{1}{2}}\right) = \left(c^{\frac{1}{2}}\right)^2}$

$\;\;\textsf\green{{ \boxed{\mathsf{\left(p^{n}\right)^m = p^{mn}}}}}$

$\: \: \: \: \: \: \: \::\implies \mathsf{\left(a^{\frac{2}{2}}\right) + \left(b^{\frac{2}{2}}\right) + 2\left(a^{\frac{1}{2}}\right)\left(b^{\frac{1}{2}}\right) = \left(c^{\frac{2}{2}}\right)}$

$\: \: \: \: \: \: \: \::\implies \mathsf{a + b + 2\left(a^{\frac{1}{2}}\right)\left(b^{\frac{1}{2}}\right) = c}$

$\: \: \: \: \: \: \: \::\implies \mathsf{a + b - c = -2\left(a^{\frac{1}{2}}\right)\left(b^{\frac{1}{2}}\right)}$

⠀⠀⠀⠀⠀$\small\underline{\pmb{\sf Squaring \: on \: both \: sides:-}}$

$\: \: \: \: \: \: \: \::\implies \mathsf{(a + b - c)^2 = (-1)^2(2)^2\left(a^{\frac{1}{2}}\right)^2\left(b^{\frac{1}{2}}\right)^2}$

$\: \: \: \: \: \: \: \::\implies \mathsf{(a + b - c)^2 = 4\left(a^{\frac{2}{2}}\right)\left(b^{\frac{2}{2}}\right)}$

$\: \: \: \: \: \: \: \:\pink{:\implies \mathsf{(a + b - c)^2 = 4ab}}$

$\therefore\:\underline{\textsf{ Value of (a + b - c)² is \textbf{4ab }}}.$