Question

-6√24+4√96. D. Calculați x + y şi x -y, unde: √18 (√192-√147 +√243-√432) si y = √48 (√72-√128 +√/288-√/162) ​

Answer 1

Răspuns:

Explicație pas cu pas:

x = √18 (√192-√147 +√243-√432)

y = √48 (√72-√128 +√/288-√/162)

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x = 3√2·(8√3 - 7√3 + 9√3 - 12√3) =

= 3√2·(-2√3) = -6√6

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y = 4√3·(6√2 - 8√2 + 12√2 - 9√2) =

= 4√3·(√2) = 4√6

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x + y = -6√6+4√6 = -2√6

x - y = -6√6 - 4√6 = -10√6

Answer 2

Calculați x + y şi x -y, unde:

x = √18 (√192-√147 +√243-√432)

y = √48 (√72-√128 +√/288-√/162).

$\it x=\sqrt{18}\cdor\sqrt3(\sqrt{64}-\sqrt{49}+\sqrt{81}-\sqrt{144})=\sqrt9\cdot\sqrt{2}\cdot\sqrt{3}(8-7+9-12)=\\ \\ =3\sqrt6\cdot(-2)=-6\sqrt6\\ \\ \\ y=\sqrt{48}\cdot\sqrt{2}(\sqrt{36}-\sqrt{64}+\sqrt{144}-\sqrt{81})=\sqrt{16}\cdot\sqrt{3}\cdot\sqrt{2}(6-8+12-9)=\\ \\ =4\sqrt6\cdot1=4\sqrt6$

$\it x+y=-6\sqrt6+4\sqrt6=-2\sqrt6\\ \\ x-y=-\6\sqrt6-4\sqrt6=-10\sqrt6$