Question

x = 2 + √3 ,find the value of x 2 + 1 x 2 .

Answer 1

${\huge{\pink{\underline{\underline{\purple{\mathbb{\bold{\mathcal{AnSwEr..}}}}}}}}}$

${\large{\blue{\bold{\underline{Given:-}}}}}$

$\implies \: x = 2 + \sqrt{ 3 }$

${\large{\blue{\bold{\underline{To\:Find:-}}}}}$

▪︎ The value of,

$\implies \: x {}^{2} + 1x + 2$

${\large{\blue{\bold{\underline{ID\:Used:-}}}}}$

▪︎ (a+b)² = a²+b²+2ab.

${\large{\blue{\bold{\underline{Now,}}}}}$

▪︎ By putting the value of x we get,

$\implies \: (2 + \sqrt{ 3 }) {}^{2} + 1(2 + \sqrt{3}) + 2 \\ \\ = (2) {}^{2} + ( \sqrt{3}) {}^{2} + 2(2)( \sqrt{3}) + 2 + \sqrt{3} + 2 \\ \\ = 4 + 3 + 4 \sqrt{3} + 2 + \sqrt{3} + 2 \\ \\ = 11 + 4 \sqrt{3} + \sqrt{3} \\ \\ = 11 + 5 \sqrt{3} .$

☆ Therefore your answer is $11 + 5 \sqrt{3} .$

Answer 2

$\huge\bold\red{Answer:-}$

${\underline{\underline{\mathsf{\pink{Given:-}}}}}$

→ $x = 2 + \sqrt{3}$

${\underline{\underline{\mathsf{\pink{To \ find:-}}}}}$

→ $x^2 + 1x + 2$

${\underline{\underline{\mathsf{\pink{Identity:-}}}}}$

→ $(a+b)^2 = a^2 + b^2 + 2ab$

${\underline{\underline{\mathsf{\blue{Solution:-}}}}}$

★ x² + 1x + 2

→ (2 + √3)² + (2+√3) + 2

→ ((2)² + (√3)² + 2×2×√3)) + (2+√3) + 2

→ (7+ 4√3) + 2+√3 + 2

→ 11 + 5√3

† ${\underline{\underline{\mathsf{\red{Here, \ the \ required</p><p>\ answer \ is:-}}}}}$ $11 + \sqrt{3}$

____________________________