Solve the equation 2y^(1/2) -7y^(1/4) +3 = 0

2y^1/2 -7y^1/4+ 3 = 0 We need to use a substitution to obtain a quadratic.Let y^1/4 = x (use the y with the smallest fractional power as your substitution)From this, we can see that y^1/2 = x² (using the laws of indices: (y^a)^b = y^ab )We substitute this in and obtain an equation in terms of x. The right hand side will stay the same as this is just equal to 0.The equation becomes:2x² -7x + 3 = 0 We can now solve this by factorizing, (2x - 1)(x -3) = 0 we now get our solutions:(2x - 1) = 0 rearranging for x we get: x = 1/2(x - 3) = 0 x = 3 Sub our values for x into the original substitution y^1/4 = x We can rearrange this substitution for y:(y^1/4)⁴ = (x)⁴y = x⁴ Now y = (1/2)⁴ = 1/16and y = (3)⁴ = 81 so the solutions of the equation are 1/16 and 81.