Question

daca a,d,c sunt nr reale astfel incat ab+ac=20 iar b+c=3radical18- 2radical8, atunci nr a este egal cu...

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Answer 1

Răspuns:

ab+ac =20

a(b+c)=20

$b + c = 3 \sqrt{18} - 2 \sqrt{8} = 3 \times 3 \sqrt{2} - 2 \times 2 \sqrt{2} = 9 \sqrt{2} - 4 \sqrt{2} = 5 \sqrt{2} \\ a(b + c) = 20 \\ a \times 5 \sqrt{2} = 20 \\ a = \frac{20}{5 \sqrt{2} } = \frac{20 \sqrt{2} }{5 \sqrt{2} \times \sqrt{2} } = \frac{20 \sqrt{2} }{10} = 2 \sqrt{2}$