10^0.7=(x^2)/(x-62)^2

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Solution for 10^0.7=(x^2)/(x-62)^2 equation: 


D( x )

(x-62)^2 = 0

(x-62)^2 = 0

(x-62)^2 = 0

x-62 = 0 // + 62

x = 62

x in (-oo:62) U (62:+oo)

10^0.7 = (x^2)/((x-62)^2) // - (x^2)/((x-62)^2)

10^0.7-((x^2)/((x-62)^2)) = 0

(-1*x^2)/((x-62)^2)+10^0.7 = 0

(-1*x^2)/((x-62)^2)+(10^0.7*(x-62)^2)/((x-62)^2) = 0

10^0.7*(x-62)^2-1*x^2 = 0

(10^0.7-1)*x^2-124*10^0.7*x+3844*10^0.7 = 0

(10^0.7-1)*x^2-124*10^0.7*x+3844*10^0.7 = 0

(10^0.7-1)*x^2-124*10^0.7*x+3844*10^0.7 = 0

DELTA = (-124*10^0.7)^2-(4*3844*(10^0.7-1)*10^0.7)

DELTA = 15376*10^1.4-15376*10^0.7*(10^0.7-1)

DELTA = 77062.5486007800055744

DELTA > 0

x = ((15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2)-(-124*10^0.7))/(2*(10^0.7-1)) or x = (-(-124*10^0.7)-(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))

x = (124*10^0.7+(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1)) or x = (124*10^0.7-(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))

(x-((124*10^0.7-(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))))*(x-((124*10^0.7+(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1)))) = 0

((x-((124*10^0.7-(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))))*(x-((124*10^0.7+(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1)))))/((x-62)^2) = 0

((x-((124*10^0.7-(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))))*(x-((124*10^0.7+(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1)))))/((x-62)^2) = 0 // * (x-62)^2

(x-((124*10^0.7-(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))))*(x-((124*10^0.7+(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1)))) = 0

( x-((124*10^0.7+(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))) )

x-((124*10^0.7+(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))) = 0 // + (124*10^0.7+(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))

x = (124*10^0.7+(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))

( x-((124*10^0.7-(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))) )

x-((124*10^0.7-(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))) = 0 // + (124*10^0.7-(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))

x = (124*10^0.7-(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1))

x in { (124*10^0.7+(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1)), (124*10^0.7-(15376*10^1.4-15376*10^0.7*(10^0.7-1))^(1/2))/(2*(10^0.7-1)) }

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