If two of LG ^ x-lgx ^ - 2 = 0 are a and B, then the value of LGB ／ LGA + LGA ／ LGB is note: ^ refers to 2

If two of LG ^ x-lgx ^ - 2 = 0 are a and B, then the value of LGB ／ LGA + LGA ／ LGB is note: ^ refers to 2

Let lgx = t
t^2-2t-2=0
lgA+lgB=2 lgA*lgB=-2
Vader's theorem (LGB) ^ 2 + (LGA) ^ 2 / LGA * LGB (LGA + LGB) ^ 2 = (LGB) ^ 2 + (LGA) ^ 2 + 2lga * LGB
4-2*（-2）/-2=-4

If (lgx) ² - lgx & #178; - 2 = 0 are a and B, find the value of LGA + LGB

The two solutions of (lgx) ^ 2-lgx ^ 2-2 = 0 are a and B,
That is, (lgx) ^ 2-2lgx-2 = 0 is a and B
Then (LGA) ^ 2-2lga-2 = 0
（lgb)^2-2lgb-2=0
So LGA and LGB are the roots of the equation m ^ 2-2m-2 = 0
That is, LGA + LGB = - B / a = - (- 2) / 1 = 2
That is, LGA + LGB = 2

The relationship between a and B when LG (a + b) = LGA + LGB holds

a+b=a*b
a=b/b-1
Take 10 as the base