Question

Ex 2
f(x)=x^2-5x+8
X1 +X2 - X1 × X2

Answer 1

 

Folosim relatiile lui Viete care, pentru a studia

functia de gradul 2, respectiv ecuatia de gradul 2, sunt:

.

$\displaystyle\bf\\Fie~functia:\\\\f(x)=ax^2+bx+c=0 \\x_1+x_2=-\frac{b}{a}\\\\ x_1x_2=\frac{c}{a}\\\\Fu7nctia~data~este:\\\\f(x)=x^2-5x+8~~~in~care:~~a=1,~b=-5~si~c=8\\\\x_1+x_2=5\\\\x_1x_2=8\\\\Rezolvare:\\\\ a)~~x_1+x_2-x_1x_2=5-8=\boxed{\bf-3}\\\\ b)~~\frac{1}{x_1}+\frac{1}{x_2}=\frac{x_2}{x_1x_2}+\frac{x_1}{x_1x_2} =\frac{x_1+x_2}{x_1x_2}=\boxed{\bf\frac{5}{8}}\\\\c)~~3(x_1+x_2)-5x_1x_2=3\cdot5-5\cdot8=15-40=\boxed{\bf-25}$