Question

calculati a) (√7+√3)(√7-√3). b)(√5-√2)²+2√2(√5-√2). c)(3+2√2)²-(3-√8)². d)(√2-√3)²-(√2-√3)(√2+√3). Plss dau coroana​

Answer 1

Răspuns:

Explicație pas cu pas:

b)

(√7 + √3)(√7 - √3)

= (√7)² - (√3)² = 7 - 3 = 4

c)

(√5 - √2)² + 2√2(√5 - √2)

= (√5)² - 2 × √5 × √2 + (√2)² + 2√10 - 2 × 2

= 5 - 2√10 + 2 + 2√10 - 4

= 5 + 2 - 4

= 3

d)

(√2 - √3)² - (√2 - √3)(√2 + √3)

= (√2)² - 2 × √2 × √3 + (√3)² - (√2)² + (√3)²

= 2 - 2√6 + 3 - 2 + 3

= - 2√6 + 6

Answer 2

Explicație pas cu pas:

a)

$( \sqrt{7} + \sqrt{3})( \sqrt{7} - \sqrt{3}) = {( \sqrt{7} )}^{2} - {( \sqrt{3} )}^{2} \\ = 7 - 3 = 4$

b)

${( \sqrt{5} - \sqrt{2})}^{2} + 2 \sqrt{2}(\sqrt{5} - \sqrt{2}) =\\= (\sqrt{5} - \sqrt{2})(\sqrt{5} - \sqrt{2} + 2 \sqrt{2}) \\ = {( \sqrt{5} )}^{2} - {( \sqrt{2} )}^{2} = 5 - 2 = 3$

c)

${(3 + 2 \sqrt{2})}^{2} - {(3 - \sqrt{8} )}^{2} = {(3 + 2 \sqrt{2})}^{2} - {(3 - 2 \sqrt{2} )}^{2} = \\ = (3 + 2 \sqrt{2} + 3 - 2 \sqrt{2})(3 + 2 \sqrt{2} - 3 + 2 \sqrt{2}) \\ = 6 \times 4 \sqrt{2} = 24 \sqrt{2}$

d)

${( \sqrt{2} - \sqrt{3})}^{2} - ( \sqrt{2} - \sqrt{3})(\sqrt{2} + \sqrt{3}) = \\ = ( \sqrt{2} - \sqrt{3})(\sqrt{2} - \sqrt{3} - \sqrt{2} - \sqrt{3}) \\ = ( \sqrt{2} - \sqrt{3})( - 2 \sqrt{3}) = - 2 \sqrt{6} + 6 \\ = 2(3 - \sqrt{6})$