Question

If x=2+√3 y=2-√3. Find the value of x^2+y^2

Answer 1

Answer:14

Step-by-step explanation:

x=2+√3

y=2-√3

x^2+y^2=(2+√3)^2+(2-√3)^2

x^2+y^2=(4+3+4√3)+(4+3-4√3)

x^2+y^2=7+7

x^2+y^2=14

Hope it helps

Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Given:

• $x = 2 + \sqrt{3}$
• $y = 2 - \sqrt{3}$

To Find:

• $Value\:of\:x^2 + y^2$

Solution:

$\implies x^2 + y^2 \\ \implies (2 + \sqrt{3})^2 + (2 - \sqrt{3})^2 \\ \implies [2^2 + (\sqrt{3})^2 + 2(2)(\sqrt{3})] + [2^2 + (\sqrt{3})^2 - 2(2)(\sqrt{3})] \\ \implies (4 + 3 + 4\sqrt{3}) + (4 + 3 - 4\sqrt{3}) \\ \implies (7 + 4\sqrt{3}) + (7 - 4\sqrt{3}) \\ \implies 7 + 4\sqrt{3}\!\!\!\!\!\!\!\!\bold{/} \:\:\: + 7 - 4\sqrt{3}\!\!\!\!\!\!\!\!\bold{/} \\ \bold {\implies 14}$

Formulae Used:

• $(a + b)^2 = a^2 + b^2 + 2ab$
• $(a - b)^2 = a^2 + b^2 - 2ab$

Hope it helps!