Решите пожалуйста 6 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!. Created by roman1311. algebra-ru

Решите пожалуйста 6 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!...

Lesben X² +10x - 4=0; 1/(x1)² +1/(x2)² = ?
1/(x1)² +1/(x2)² = (x1² +x2²)/(x1²*x2²) (***)
по теореме Виета: x1*x2 = - 4 --> x1²*x2² =16 (*)
x1+x2 = -10 (возводим в квадрат обе части ур-я)
(x1+x2)² =100 --> x1²+x2² = 100 -2x1*x2 -->
x1²+x2² =100 +8 =108 (**)
(*) и (**) подставляем в (***)
1/x1² +1/x2² = 108/16 =6,75 ответ 6,75

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ludmilagena

Verified answer

Xˇ2+10x-4=0
x1+x2=-10,x1.x2=-4
(x1+x2)ˇ2=x1ˇ2+2x1.x2+x2ˇ2=100
x1ˇ+xˇ2=100-2.x1.x2=100-2.(-4)=100+8=108
1/x1ˇ2 +1/x2ˇ2= (x1ˇ2+x2ˇ2)/x1ˇ2.x2ˇ2=
=108/(-4)ˇ2=108/16=27/4

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