Question

M. Calculați folosind formulele de calcu a) (3-√2); (2-√3)²; (4+ √2); b) (4-√3); (5-√√2): (√5 +√3): c)(√5-√2): (√5 +√7); (√3+2); d) (3-√5); (√3-√2); (√6+2) ; e) (√3-√2)(√3+√2)+(√5-3)(√5 + 3); 1) (√6-√3)(√6 +√3)(√6-√10)(√6 +√10). urtot: repede dau corona ​

Answer 1

Răspuns:

$a) {(3 - \sqrt{2} })^{2} = {3}^{2} - 2 \times 3 \times \sqrt{2} + (\sqrt{2} ) ^{2} = 9 - 6 \sqrt{2} + 2 = 11 - 6 \sqrt{2 } \\ {(2 - \sqrt{3} })^{2} = {2}^{2} - 2 \times 2 \times \sqrt{3} + ({ \sqrt{3} })^{2} = 4 - 4 \sqrt{3} + 3 = 7 - 4 \sqrt{3} \\ {(4 + \sqrt{2} })^{2} = {4}^{2} + 2 \times 4 \times \sqrt{2} + ({ \sqrt{2} })^{2} = 16 + 8 \sqrt{2} + 2 = 18 + 8 \sqrt{2}$

$b) {(4 - \sqrt{3} })^{2} = {4}^{2} - 2 \times 4 \times \sqrt{3} + ( { \sqrt{3} })^{2} = 16 - 8 \sqrt{3} + 3 = 19 - 8 \sqrt{3} \\ {(5 - \sqrt{2} })^{2} = {5}^{2} - 2 \times 5 \times \sqrt{2} + ( { \sqrt{2} })^{2} = 25 - 10 \sqrt{2} +2 = 27 - 10 \sqrt{2} \\ ({ \sqrt{5} + \sqrt{3} })^{2} = ( { \sqrt{5} })^{2} + 2 \times \sqrt{5} \times \sqrt{3} + ({ \sqrt{3} })^{2} = 5 + 2 \sqrt{15} + 3 = 8 + 2 \sqrt{15}$

$c) {( \sqrt{5} - \sqrt{2} })^{2} = ({ \sqrt{5} })^{2} - 2 \times \sqrt{5} \times \sqrt{2} + ({ \sqrt{2} })^{2} = 5 - 2 \sqrt{10} + 2 = 7 - 2 \sqrt{10} \\ ({ \sqrt{5} + \sqrt{7} })^{2} = ({ \sqrt{5} })^{2} + 2 \times \sqrt{5} \times \sqrt{7} + ({ \sqrt{7} })^{2} = 5 + 2 \sqrt{35} + 7 = 12 + 2 \sqrt{35} \\ ({ \sqrt{3} + 2 })^{2} = ( { \sqrt{3} })^{2} + 2 \times \sqrt{3} \times 2 + {2}^{2} = 3 + 4 \sqrt{3} + 4 = 7 + 4 \sqrt{3}$

$d) ({( 3 - \sqrt{5} })^{2} = {3}^{2} - 2 \times 3 \times \sqrt{5} + ( { \sqrt{5} })^{2} = 9 - 6 \sqrt{5} + 5 = 14 - 6 \sqrt{5} \\( { \sqrt{3} - \sqrt{2} })^{2} = ({ \sqrt{3} })^{2} - 2 \times \sqrt{3} \times \sqrt{2} + ({ \sqrt{2} })^{2} = 3 - 2 \sqrt{6} + 2 = 5 - 2 \sqrt{6} \\ ({ \sqrt{6} + 2 })^{2} = ({ \sqrt{6} })^{2} + 2 \times \sqrt{6} \times 2 + {2}^{2} = 6 + 4 \sqrt{6} + 4 = 10 + 4 \sqrt{6}$

$e)( \sqrt{3} - \sqrt{2} )( \sqrt{3} + \sqrt{2}) + ( \sqrt{5} - 3)( \sqrt{5} + 3) = ({ \sqrt{3} })^{2} - ( { \sqrt{2} })^{2} + ({ \sqrt{5} })^{2} - {3}^{2} = 3 - 2 + 5 - 9 = - 3$

$f)( \sqrt{6} - \sqrt{ 3} )( \sqrt{6} + \sqrt{3} ) - ( \sqrt{6} - \sqrt{10} )( \sqrt{6} + \sqrt{10} ) = \\ = ({ \sqrt{6} })^{2} - ( { \sqrt{3} })^{2} - ( ({ \sqrt{6} })^{2} - ( { \sqrt{10} })^{2} ) = \\ = 6 - 3 - (6 - 10) = 3 - ( - 4) = 3 + 4 = 7$