Solve the Given Square Root Question
Solve it. Square root (3x - 17^3/4) - square root (2x - 13^3/4) = 1
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Sqrt (3x - 17^(3/4)) - sqrt (2x - 13^(3/4)) = 1 gives newlinesqrt(3x - 17^(3/4)) = sqrt (2x - 13^(3/4)) + 1 gives newline3x - 17^(3/4) = 2x - 13^(3/4) + 1 +2 sqrt (2x - 13^(3/4)) gives newline x - 17^(3/4) + 13^(3/4) - 1 = 2 sqrt (2x - 13^(3/4)) newline(x - 17^(3/4) + 13^(3/4) - 1 )^2= 4 (2x - 13^(3/4)) newlinex^2 -2(17^(3/4) - 13^(3/4) + 1)x + (17^(3/4) - 13^(3/4) + 1)^2 = 4 (2x - 13^(3/4)) newlinex^2 -2(17^(3/4) - 13^(3/4) - 3)x + (17^(3/4) - 13^(3/4) + 1)^2+ 4*13^(3/4)= 0 newlinex^2 -2(17^(3/4) - 13^(3/4) - 3)x + (17^(3/2) + 13^(3/2) + 1-2(17*13)^(3/4)-2*13^(3/4) + 17^(3/4))^2+ 4*13^(3/4)+4*13^(3/4)= 0 newlineΔ = 4(17^(3/4) - 13^(3/4) - 3)^2 -4((17^(3/2) + 13^(3/2) + 1-2(17*13)^(3/4)-2*13^(3/4) + 17^(3/4))^2+ 4*13^(3/4)+4*13^(3/4)) need "to" be checked with calculator "to" see if it is positive "or" newline negative "and" take into consideration also that x >= 13^(3/4)/2 "and" x >= 17^(3/4)/3
Sqrt (3x - 17^(3/4)) - sqrt (2x - 13^(3/4)) = 1 gives newlinesqrt(3x - 17^(3/4)) = sqrt (2x - 13^(3/4)) + 1 gives newline3x - 17^(3/4) = 2x - 13^(3/4) + 1 +2 sqrt (2x - 13^(3/4)) gives newline x - 17^(3/4) + 13^(3/4) - 1 = 2 sqrt (2x - 13^(3/4)) newline(x - 17^(3/4) + 13^(3/4) - 1 )^2= 4 (2x - 13^(3/4)) newlinex^2 -2(17^(3/4) - 13^(3/4) + 1)x + (17^(3/4) - 13^(3/4) + 1)^2 = 4 (2x - 13^(3/4)) newlinex^2 -2(17^(3/4) - 13^(3/4) - 3)x + (17^(3/4) - 13^(3/4) + 1)^2+ 4*13^(3/4)= 0 newlinex^2 -2(17^(3/4) - 13^(3/4) - 3)x + (17^(3/2) + 13^(3/2) + 1-2(17*13)^(3/4)-2*13^(3/4) + 17^(3/4))^2+ 4*13^(3/4)+4*13^(3/4)= 0 newlineΔ = 4(17^(3/4) - 13^(3/4) - 3)^2 -4((17^(3/2) + 13^(3/2) + 1-2(17*13)^(3/4)-2*13^(3/4) + 17^(3/4))^2+ 4*13^(3/4)+4*13^(3/4)) need "to" be checked with calculator "to" see if it is positive "or" newline negative "and" take into consideration also that x >= 13^(3/4)/2 "and" x >= 17^(3/4)/3
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