If √ax²-b=c and a=2, b=7, and e=5, find X
sqrt(ax^2 - b) = c,
sqrt(2x^2 - 7) = 5,
Square both sides:
2x^2 - 7 = 25,
2x^2 = 25 + 7,
2x^2 = 32,
x^2 = 32 /2 = 16,
Take sqrt of both sides and get:
x = +- 4.
To find the value of x in the equation √(ax² - b) = c, given that a = 2, b = 7, and c = 5, we can substitute these values into the equation and solve for x.
Step 1: Substitute the given values into the equation:
√(2x² - 7) = 5
Step 2: Square both sides of the equation to remove the square root:
(√(2x² - 7))^2 = 5^2
2x² - 7 = 25
Step 3: Add 7 to both sides of the equation:
2x² = 25 + 7
2x² = 32
Step 4: Divide both sides of the equation by 2 to isolate x²:
x² = 32 / 2
x² = 16
Step 5: Take the square root of both sides to solve for x:
x = ±√16
Step 6: Simplify the square root:
x = ±4
Therefore, the values of x that satisfy the equation √(2x² - 7) = 5 are x = 4 and x = -4.