Question

Fie numarul x=(√2+√3)la a2 +(1-√6)(1+√6).Aratati ca x < 5.

Answer 1

(a+b)² = a²+2ab+b²
(√2+√3)la a2 = (√2)² + 2√6 + (√3)² = 2 + 2√6 + 3 = 5 + 2√6
(a-b)(a+b) = a² - b²
(1-√6)(1+√6) = 1² - (√6)² = 1 - 6 = - 5

x=5 + 2√6 + (-5) = 5 + 2√6 - 5 = 2√6 < 5
x < 5

Answer 2

[tex]\it x = (\sqrt2-\sqrt3)^2 +(1-\sqrt6)(1+\sqrt6) = 2+2\sqrt6 +3+1-6 = \\ \\ =2\sqrt6 = \sqrt{24} \ \textless \ \sqrt{25} = 5[/tex]