Question

Calculați x + y și x - y în următoarele cazuri :​

Answer 1

Răspuns:

$a) \: x = 3 \sqrt{8} - 4 \sqrt{50} - \sqrt{27} \\ x = 3 \times 2 \sqrt{2} - 4 \times 5 \sqrt{2} - 3 \sqrt{3} \\ x = 6 \sqrt{2} - 20 \sqrt{2} - 3 \sqrt{3} = - 14 \sqrt{2} - 3 \sqrt{3}$

$y = 3 \sqrt{48} - \sqrt{98} - 2 \sqrt{75} \\ y = 3 \times 4 \sqrt{3} - 7 \sqrt{2} - 2 \times 5 \sqrt{3} \\ y = 12 \sqrt{3} - 7 \sqrt{2} - 10 \sqrt{3} = - 7 \sqrt{2} + 2 \sqrt{3}$

$x + y = ( - 14 \sqrt{2} - 3 \sqrt{3} ) + ( - 7 \sqrt{2} + 2 \sqrt{3} ) = - 14 \sqrt{2} - 3 \sqrt{3} - 7 \sqrt{2} + 2 \sqrt{3} = - 21 \sqrt{2} - \sqrt{3}$

$x - y = ( - 14 \sqrt{2} - 3 \sqrt{3} ) - ( - 7 \sqrt{2} + 2 \sqrt{3} ) \\ x - y = - 14 \sqrt{2} - 3 \sqrt{3} + 7 \sqrt{2} - 2 \sqrt{3} = - 7 \sqrt{2} - 5 \sqrt{3}$

$b)x = 5 \sqrt{8} - \sqrt{20} - 4 \sqrt{45} \\ x = 5 \times 2 \sqrt{2} - 2 \sqrt{5} - 4 \times 3 \sqrt{5} \\ x = 10 \sqrt{2} - 2 \sqrt{5} - 12 \sqrt{5} = 10 \sqrt{2} - 14 \sqrt{5}$

$y = 7 \sqrt{18} - \sqrt{125} - 3 \sqrt{98} \\ y = 7 \times 3 \sqrt{2} - 5 \sqrt{5} - 3 \times 7 \sqrt{2} \\ y = 21 \sqrt{2} - 5 \sqrt{5} - 21 \sqrt{2} = - 5 \sqrt{5}$

$x + y = (10 \sqrt{2} - 14 \sqrt{5}) + ( - 5 \sqrt{5}) \\ x + y = 10 \sqrt{2} - 14 \sqrt{5} - 5 \sqrt{5} = 10 \sqrt{2} - 19 \sqrt{5}$

$x - y = (10 \sqrt{2} - 14 \sqrt{5}) - ( - 5 \sqrt{5} ) \\ x - y = 10 \sqrt{2} - 14 \sqrt{5} + 5 \sqrt{5} = 10 \sqrt{2} - 9 \sqrt{5}$