Question

问一道初一完全平方公式的题如果答得好 最后加100悬赏分题目见下图：答案最好也是以图片的形式 展现出来

Answer 1

(1)X^2+1/X^2=(X+1/X)^2-(2)=(X-1/X)^2+(2)

(2)若a+1/a=5,则a^2+1/a^2的值是多少?

则：a^2+1/a^2=(a+1/a)^2-2=5^2-2=23

(3)若a^2-3a+1=0,则a^2+1/a^2的值是多少?

a1=3/2+(9/4-1)^0.5=3/2+(5/4)^0.5=3/2+5^0.5/2=(3+5^0.5)/2

a+1/a=(3+5^0.5)/2+1/((3+5^0.5)/2)

=(3+5^0.5)/2+2/(3+5^0.5)

=((3+5^0.5)^2+4)/(2*(3+5^0.5))

=(9+6*(5^0.5)+5+4)/(6+2*(5^0.5))

=(18+6*(5^0.5))/(6+2*(5^0.5))

=(9+3*(5^0.5))/(3+(5^0.5))

=3*(3+(5^0.5))/(3+(5^0.5))

=3

a^2+1/a^2=(a+1/a)^2-2

=3^2-2

=7

a2=3/2-(9/4-1)^0.5=3/2-(5/4)^0.5=3/2-5^0.5/2=(3-5^0.5)/2

a+1/a=(3-5^0.5)/2+1/((3-5^0.5)/2)

=(3-5^0.5)/2+2/(3-5^0.5)

=((3-5^0.5)^2+4)/(2*(3-5^0.5))

=(9-6*(5^0.5)+5+4)/(6-2*(5^0.5))

=(18-6*(5^0.5))/(6-2*(5^0.5))

=6*(3-(5^0.5))/2*(3-(5^0.5))

=6*(3-(5^0.5))/2*(3-(5^0.5))

=3

a^2+1/a^2=(a+1/a)^2-2

=3^2-2

=7