Task/26381185
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N1.
x² +81x²/(x+9)² = 40 ;
(x - 9x/(x+9) ) ² +2x*9x/(x+9) - 40 =0 ;
( x²/(x+9) ) ² +18* x²/(x+9) - 40 = 0 ; * * * t = x²/(x+9) * * *
x²/(x+9)= -20 или x²/(x+9) =2 .
a)
x²/(x+9) = - 20 ;
x²+ 20x +180 =0 ; не имеет действительных корней
* * * (x+ 10)² +80 =0 * * *
b)
x²/(x+9) = 2;
x²- 2x - 18 =0 ;
x²- 2x - 18 =0 ;
x₁ = 1 -√19 ;
x₂ = 1 +√19 .
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N2.
( 4x /(x+1) )² +( 4x /(x - 1) )² = 45 ;
( 4x / (x+1) + 4x /(x - 1) )² - 2*4x(x+1)*4x /(x - 1) ) =45 ;
64*(x²/(x² -1) )² - 32*x²/(x² -1) - 45 = 0 ; * * * t =x²/(x² -1) * * *
x²/(x² -1)= - 5/8 или x²/(x² -1) =9/8.
a)
x²/(x² -1) = - 5/8 ;
8x² = -5x² +5
x₁,₂ = ± (√65) / 13
b)
x²/(x² -1) = 9/8 ;
8x² =9x² - 9 ;
x² =9 ;
x₃,₄ = ±3.
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N3.
(x²+1/x²)+7(x-1/x) +10 =0 ;
(x-1/x)² +7(x+1/x) + 12 =0 ; * * * t =(x+1/x) * * *
x+1/x = - 3 или x+1/x = - 4 .
a)
x+ 1/x = - 3 ;
x² +3x +1 =0 ;
x₁,₂ = (-3±√5) / 2 .
b)
x+ 1/x = - 4 ;
x² +4x +1 =0 ;
x₃,₄ = (-2±√3) / 2.
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N4.
(x²+1/x²) - 7(x+1/x) +9 =0 ;
(x+1/x)² - 7(x+1/x) + 7 =0 ; * * * t =x+1/x * * *
t² -7t +7 =0 ; D =7² -4*7 =49 -28 =21.
t =(7 ±√21) / 2 ;
t₁ = (7 - √21) / 2;
t₂ = (7 +√21) / 2 .
x+1/x = (7- √21)/ 2 или x+1/x = (7+ √21)/ 2 .
a)
x+ 1/x = (7- √21)/ 2;
2x² -(7 - √21)x +2 =0 ; D < 0 → не имеет действительных корней <br>b)
x+ 1/x = (7+ √21)/ 2 ;
2x² - (7+ √21)x +2 =0 ; D =(7+ √21)² - 4*2*2 = 54 +14√21 ;
x₃,₄ = (7+ √21 ± √(54 +14√21)/ 4.
нужно проверить арифметику