Question

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Answer 1

Răspuns:

Explicație pas cu pas:

a=3√2(4√6-8√3-6√6+12√6)=3√2(10√6-8√3)=30×2√3-24√6=12√3(5-2√2)

b=2√3(-6√6-5√6+9√3+8√6)=2√3(9√3-3√6)=2×3×3(3-√2)=18(3-√2)

Answer 2

$\displaystyle a=\sqrt{18}(\sqrt{96}-\sqrt{192}-\sqrt{216}+\sqrt{432})\\ \\ a=3\sqrt{2}(4\sqrt{6}-8\sqrt{3}-6\sqrt{6}+12\sqrt{3})\\ \\ a=12\sqrt{12}-24\sqrt{6}-18\sqrt{12} +36\sqrt{6}\\ \\ a=12\cdot2\sqrt{3}-24\sqrt{6}-18\cdot2\sqrt{3} +36\sqrt{6}\\ \\ a=24\sqrt{3} -24\sqrt{6}-36\sqrt{3}+36\sqrt{6}\\ \\ a=12\sqrt{6} -12\sqrt{3} \\ \\ \mathbf{a=12(\sqrt{6}-\sqrt{3} )}$

$\displaystyle b=\sqrt{12}(-\sqrt{108}-\sqrt{150}+\sqrt{243}+\sqrt{384})\\ \\ b=2\sqrt{3}(-6\sqrt{3}-5\sqrt{6}+9\sqrt{3}+8\sqrt{6})\\ \\ b=-12\sqrt{9}-10\sqrt{18} +18\sqrt{9} +16\sqrt{18} \\ \\ b=-12\cdot3-10\cdot  3\sqrt{2}+18\cdot3+16\cdot 3\sqrt{2}\\ \\ b=-36-30\sqrt{2}  +54+48\sqrt{2} \\ \\ b=18+18\sqrt{2}\\ \\ \mathbf{b=18(1+\sqrt{2})}$