Find the real solutions of the equation. (Round your answers to three decimal places. Enter your answers as a comma-separated list.)
3.8x4 − 1.7x2 = 2.8
you probably meant:
3.8x^4 − 1.7x^2 = 2.8
multiply each term by 10
38x^4 - 17x^2 - 28 = 0
let y =x^2
38y^2 - 17y - 28 = 0 , since b^2 - 4ac is not a perfect square, it will not factor
so
y = (17 ± √4545)/76 = ...
reject the negative answer,
take √ of the positive result, for ± x
A motor car is uniformly retarded and brought to rest form a speed of 108km/h in 15 seconds.find its retardation
To find the real solutions of the equation 3.8x^4 - 1.7x^2 = 2.8, we need to solve for x. Here's how you can do it:
1. Start by rearranging the equation to form a quadratic equation in terms of x^2. Let's substitute y = x^2:
3.8y^2 - 1.7y = 2.8
2. Now, rewrite the equation in the standard quadratic form by moving all the terms to one side:
3.8y^2 - 1.7y - 2.8 = 0
3. Next, solve the quadratic equation. You can use various methods to solve it, like factoring, completing the square, or using the quadratic formula. The quadratic formula is often the most convenient method for solving quadratic equations. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 3.8, b = -1.7, and c = -2.8.
4. Plug these values into the quadratic formula and solve for x:
x = (-(-1.7) ± √((-1.7)^2 - 4 * 3.8 * (-2.8))) / (2 * 3.8)
= (1.7 ± √(2.89 + 42.56)) / 7.6
= (1.7 ± √45.45) / 7.6
5. Calculate √45.45, which is approximately 6.745.
6. Substitute this value back into the equation:
x = (1.7 ± 6.745) / 7.6
7. Now, calculate the two possible solutions:
x1 = (1.7 + 6.745) / 7.6
= 8.445 / 7.6
≈ 1.111
x2 = (1.7 - 6.745) / 7.6
= -5.045 / 7.6
≈ -0.664
So, the real solutions of the equation 3.8x^4 - 1.7x^2 = 2.8, rounded to three decimal places, are approximately 1.111 and -0.664.