x+y+√z=148
x+√y+z=82
√x+y+z=98
find x,y,z given that x,y,z are all
positive integers.
Please i need the solution
#thanks
To me, the actual solution is less important than the method of getting that solution.
We should assume that all values would be whole numbers. More than that, all numbers would have to be perfect squares or else we would have decimals
suppose we subtract the second from the third:
√x - x + y - √y = 16
y-x + √x-√y = 16
does that give you any ideas?
So, there is no solution?
To find the values of x, y, and z, we'll solve the system of equations step by step.
Given equations:
1. x + y + √z = 148
2. x + √y + z = 82
3. √x + y + z = 98
Step 1: Let's isolate √z in the first equation:
x + y + √z = 148
√z = 148 - x - y
Step 2: Square both sides of the equation obtained in Step 1 to eliminate the square root:
z = (148 - x - y)^2
Step 3: Substitute the expression for z from Step 2 into the second equation:
x + √y + (148 - x - y)^2 = 82
Step 4: Simplify the equation obtained in Step 3:
√y + (148 - x - y)^2 = 82 - x
Step 5: Let's isolate √y in the equation obtained in Step 4:
√y = 82 - x - (148 - x - y)^2
Step 6: Square both sides of the equation obtained in Step 5 to eliminate the square root:
y = (82 - x - (148 - x - y)^2)^2
Step 7: Substitute the expressions for z and y obtained in Step 2 and Step 6, respectively, into the third equation:
√x + (82 - x - (148 - x - y)^2)^2 + (148 - x - y)^2 = 98
Step 8: Simplify the equation obtained in Step 7:
√x + (82 - x - (148 - x - (82 - x - (148 - x - y)^2)^2)^2 + (148 - x - (82 - x - (148 - x - y)^2)^2)^2 = 98
Step 9: Solve the equation obtained in Step 8 for all possible positive integer values of x, y, and z.
Unfortunately, solving this equation to find the exact values of x, y, and z is quite complex and may require advanced mathematical techniques. Therefore, I recommend using a numeric method, such as numerical approximation or solving using a computer program, to find the approximate values of x, y, and z.