известно что a+b/a-b=7. вычислите а²+5b²/a²-4b². Created by smishleni. algebra-ru

a²-4b²...

mmb1

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(a+b)/(a-b)=7.

вычислите (а²+5b²)/(a²-4b²)

a ≠ 0 b ≠ 0

a + b = 7(a - b)

a + b = 7a - 7b

6a = 8b

a/b = 4/3

(а²+5b²)/(a²-4b²) | : b²

(а²+5b²)/b² : (a²-4b²)/b² = ((a/b)² + 5) : ((a/b)² - 4) = ((4/3)² + 5) : ((4/3)² - 4) = (16/9 + 45/9) : (16/9 - 36/9) = - 61/20

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Universalka

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$\dfrac{a+b}{a-b} =7\\\\a+b=7\cdot(a-b)\\\\a+b=7a-7b\\\\b+7b=7a-a\\\\8b=6a\\\\a=\dfrac{4}{3}b\\\\\\\dfrac{a^{2} +5b^{2} }{a^{2} -4b^{2} } =\dfrac{(\frac{4}{3}b)^{2} +5b^{2}}{(\frac{4}{3}b)^{2} -4b^{2}} =\dfrac{\frac{16}{9} b^{2}+\frac{45}{9} b^{2}}{\frac{16}{9} b{^2}-\frac{36}{9} b^{2} } =\\\\\\=\dfrac{61}{9} b^{2} :\Big(-\dfrac{20}{9} b^{2}\Big)=-\dfrac{61\cdot 9}{9\cdot 20} =\boxed{-3,05}$

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