Свойство членов геом. прогрессии: а,в,с,... - геом. прогр. ⇒ в²=ас(√х+1)²=√(х-1) *√(2х+5) х+1=√(2х²+5х-2х-5) (х+1)²= 2х²+3х-5 х²+2х+1=2х²+3х-5х²+х-6=0По теореме Виета х₁=-3, х₂=2<span>Свойство это основано на том, что q=b/a=c/b ⇒ b*b=a*c , b²=ac</span>
X=-b/2a=4/(-2)=-2
y(-2)=-4+8+5=9
y(max)=9
<span>2) 12cb</span>²<span>/9bc</span>³ = 4b/3c²
![\frac{12c b^{2} }{9b c^{3} } = \frac{4 b^{2-1} }{3 c^{3-1} } = \frac{4b}{3 c^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7B12c+b%5E%7B2%7D+%7D%7B9b+c%5E%7B3%7D+%7D+%3D++%5Cfrac%7B4+b%5E%7B2-1%7D+%7D%7B3+c%5E%7B3-1%7D+%7D+%3D+%5Cfrac%7B4b%7D%7B3+c%5E%7B2%7D+%7D+)
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3) 12ay</span>³<span>/-8a</span>²<span>y = - 3y</span>²/2a
![\frac{12a y^{3} }{-8 a^{2} y} =- \frac{3 y^{3-1} }{2a^{2-1} } =- \frac{3 y^{2} }{2a}](https://tex.z-dn.net/?f=+%5Cfrac%7B12a+y%5E%7B3%7D+%7D%7B-8+a%5E%7B2%7D+y%7D+%3D-+%5Cfrac%7B3+y%5E%7B3-1%7D+%7D%7B2a%5E%7B2-1%7D+%7D+%3D-+%5Cfrac%7B3+y%5E%7B2%7D+%7D%7B2a%7D+)
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4) -6p</span>³<span>q/-12q</span>³ = p³/2q²
![\frac{-6 p^{3} q}{-12 q^{3} } = \frac{ p^{3} }{2 q^{3-1} } = \frac{ p^{3} }{2 q^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7B-6+p%5E%7B3%7D+q%7D%7B-12+q%5E%7B3%7D+%7D+%3D+%5Cfrac%7B+p%5E%7B3%7D+%7D%7B2+q%5E%7B3-1%7D+%7D+%3D+%5Cfrac%7B+p%5E%7B3%7D+%7D%7B2+q%5E%7B2%7D+%7D+)
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5) -4ax</span>²<span>/12xy = - ax/3y
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![\frac{-4a x^{2} }{12xy} =- \frac{a x^{2-1} }{ 3y} =- \frac{ax}{3y}](https://tex.z-dn.net/?f=+%5Cfrac%7B-4a+x%5E%7B2%7D+%7D%7B12xy%7D+%3D-+%5Cfrac%7Ba++x%5E%7B2-1%7D+%7D%7B+3y%7D+%3D-+%5Cfrac%7Bax%7D%7B3y%7D+)
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6) 9axy</span>²<span>/6ay</span>³ = 3x/2y
![\frac{9ax y^{2} }{6a y^{3} } = \frac{3x}{2 y^{3-2} } = \frac{3x}{2y}](https://tex.z-dn.net/?f=+%5Cfrac%7B9ax+y%5E%7B2%7D+%7D%7B6a+y%5E%7B3%7D+%7D+%3D+%5Cfrac%7B3x%7D%7B2+y%5E%7B3-2%7D+%7D+%3D+%5Cfrac%7B3x%7D%7B2y%7D+)
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7) 48a</span>²<span>c</span>²<span>/38ac = 24ac/19
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![\frac{48 a^{2} c^{2} }{38ac} = \frac{24*2*a*a*c*c}{19*2*a*c} = \frac{24ac}{19}](https://tex.z-dn.net/?f=+%5Cfrac%7B48+a%5E%7B2%7D++c%5E%7B2%7D+%7D%7B38ac%7D+%3D+%5Cfrac%7B24%2A2%2Aa%2Aa%2Ac%2Ac%7D%7B19%2A2%2Aa%2Ac%7D+%3D+%5Cfrac%7B24ac%7D%7B19%7D+)
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8) 63x</span>³<span>y</span>⁵<span>/84x</span>⁶<span>y</span>⁴ = 3y/4x³
![\frac{63 x^{3} y^{5} }{84 x^{6} y^{4} } = \frac{21*3* y^{5-4} }{21*4* x^{6-3} } = \frac{3y}{4 x^{3} }](https://tex.z-dn.net/?f=+%5Cfrac%7B63+x%5E%7B3%7D++y%5E%7B5%7D+%7D%7B84+x%5E%7B6%7D++y%5E%7B4%7D+%7D+%3D+%5Cfrac%7B21%2A3%2A+y%5E%7B5-4%7D+%7D%7B21%2A4%2A+x%5E%7B6-3%7D+%7D+%3D+%5Cfrac%7B3y%7D%7B4+x%5E%7B3%7D+%7D+)
81/9*21*21-9/-21=1/49+3/7=22/49