Show that 3x + 4x = 5x has exactly one real root
Question
Show that 3x + 4x = 5x has exactly one real root
Solution 1
To show that the equation 3x + 4x = 5x has exactly one real root, we can follow these steps:
Step 1: Simplify the equation by combining like terms on the left side: 3x + 4x = 5x 7x = 5x
Step 2: Subtract 5x from both sides of the equation to isolate the variable: 7x - 5x = 5x - 5x 2x = 0
Step 3: Divide both sides of the equation by 2 to solve for x: 2x/2 = 0/2 x = 0
Step 4: Check if x = 0 is a real root by substituting it back into the original equation: 3(0) + 4(0) = 5(0) 0 + 0 = 0
Since the equation is true when x = 0, we can conclude that x = 0 is the only real root of the equation 3x + 4x = 5x.
Solution 2
To show that the equation 3x + 4x = 5x has exactly one real root, we can follow these steps:
Step 1: Simplify the equation by combining like terms on the left side: 3x + 4x = 5x 7x = 5x
Step 2: Subtract 5x from both sides of the equation to isolate the variable: 7x - 5x = 5x - 5x 2x = 0
Step 3: Divide both sides of the equation by 2 to solve for x: 2x/2 = 0/2 x = 0
Step 4: Check if x = 0 is a real root by substituting it back into the original equation: 3(0) + 4(0) = 5(0) 0 + 0 = 0
Since the equation is true when x = 0, we can conclude that x = 0 is the only real root of the equation 3x + 4x = 5x.
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