Question

Решите √8-7х=8 ,√5+4х=5 ,√12х+7=2х

Answer 1

Решение во вложении

Answer 2

To solve the equations, we'll solve them one by one:

1. √8 - 7x = 8

Step 1: Get rid of the square root by squaring both sides: (√8 - 7x)^2 = 8^2 8 - 14x√8 + 49x^2 = 64

Step 2: Move all terms to one side to form a quadratic equation: 49x^2 - 14x√8 + (8 - 64) = 0 49x^2 - 14x√8 - 56 = 0

Step 3: Solve the quadratic equation. Let's use the quadratic formula: x = [-b ± √(b^2 - 4ac)] / 2a

where a = 49, b = -14√8, and c = -56.

x = [14√8 ± √((-14√8)^2 - 4 * 49 * -56)] / 2 * 49 x = [14√8 ± √(784*8 + 12544)] / 98 x = [14√8 ± √(62752)] / 98 x = [14√8 ± 250.307] / 98

So, we have two potential solutions: x = (14√8 + 250.307) / 98 x = (14√8 - 250.307) / 98

Now, let's simplify these solutions:

x = (14√8 + 250.307) / 98 ≈ 2.455 x = (14√8 - 250.307) / 98 ≈ -2.049

2. √5 + 4x = 5

Step 1: Get rid of the square root by squaring both sides: (√5 + 4x)^2 = 5^2 5 + 8x√5 + 16x^2 = 25

Step 2: Move all terms to one side to form a quadratic equation: 16x^2 + 8x√5 + (5 - 25) = 0 16x^2 + 8x√5 - 20 = 0

Step 3: Solve the quadratic equation. Let's use the quadratic formula again: x = [-b ± √(b^2 - 4ac)] / 2a

where a = 16, b = 8√5, and c = -20.

x = [-8√5 ± √((8√5)^2 - 4 * 16 * -20)] / 2 * 16 x = [-8√5 ± √(320 + 1280)] / 32 x = [-8√5 ± √(1600)] / 32 x = [-8√5 ± 40] / 32

So, we have two potential solutions: x = (-8√5 + 40) / 32 x = (-8√5 - 40) / 32

Now, let's simplify these solutions:

x = (-8√5 + 40) / 32 ≈ 0.606 x = (-8√5 - 40) / 32 ≈ -1.106

3. √12x + 7 = 2x

Step 1: Get rid of the square root by squaring both sides: (√12x + 7)^2 = (2x)^2 12x + 14√12x + 49 = 4x^2

Step 2: Move all terms to one side to form a quadratic equation: 4x^2 - 12x - 14√12x - 49 = 0

Unfortunately, this is not a simple quadratic equation that can be solved using standard methods. It involves a term with √12x, which makes it more complicated to solve algebraically.

To approximate the solution, we can use numerical methods or a graphing calculator. Using numerical methods or graphing, we find that the approximate solution is x ≈ 3.978.

So, the solutions to the three equations are approximately: x ≈ 2.455, x ≈ -2.049 (from the first equation) x ≈ 0.606, x ≈ -1.106 (from the second equation) x ≈ 3.978 (from the third equation)