6. a) (4x+3)²= (4x+7)² 7. a) (√7+√5)² 60+10/35 8. a)

Ответ: 6. a) x = -5/4; 7. a) \[ \frac{\sqrt{7} + \sqrt{5}}{5} \]; 8. a) \(\sqrt{4.2}\)

Решение:

6. a)\[(4x+3)^2 = (4x+7)^2\]\[(4x+3)^2 - (4x+7)^2 = 0\]\[((4x+3) - (4x+7))((4x+3) + (4x+7)) = 0\]\[(4x+3 - 4x - 7)(4x+3 + 4x+7) = 0\]\[(-4)(8x+10) = 0\]\[8x+10 = 0\]\[8x = -10\]\[x = -\frac{10}{8} = -\frac{5}{4}\]

7. a)\[\frac{(\sqrt{7}+\sqrt{5})^2}{60+10\sqrt{35}} = \frac{7 + 2\sqrt{35} + 5}{60+10\sqrt{35}} = \frac{12 + 2\sqrt{35}}{60+10\sqrt{35}} = \frac{2(6 + \sqrt{35})}{10(6+\sqrt{35})} = \frac{2}{10} = \frac{1}{5}\]

Домножим числитель и знаменатель на сопряженное выражение к числителю: \[\frac{1}{5} = \frac{\sqrt{7} - \sqrt{5}}{5(\sqrt{7} - \sqrt{5})} = \frac{\sqrt{7} - \sqrt{5}}{5}\]

8. a)\[\frac{1.2\cdot\sqrt{1.4}}{\sqrt{0.42}} = \frac{1.2\cdot\sqrt{1.4}}{\sqrt{0.42}} = \frac{1.2\cdot\sqrt{1.4}}{\sqrt{0.3 \cdot 1.4}} = \frac{1.2}{\sqrt{0.3}} = \frac{1.2}{\sqrt{\frac{3}{10}}} = \frac{1.2}{\frac{\sqrt{3}}{\sqrt{10}}} = \frac{1.2\sqrt{10}}{\sqrt{3}} = \frac{1.2\sqrt{30}}{3} = 0.4\sqrt{30} = \sqrt{0.16 \cdot 30} = \sqrt{4.8}\]

Ответ: 6. a) x = -5/4; 7. a) \[ \frac{\sqrt{7} + \sqrt{5}}{5} \]; 8. a) \(\sqrt{4.2}\)