Question

3(x^2+ 1\x^2)+5(x+1\x)=16

Answer 1

Ответ:

3х² -8х + 13 = (х-5)²

3х² - 8х + 13 = х² - 10х + 25

3х² - 8х + 13 - х² + 10х - 25 =0

2х² +2х -12 = 0                             |÷2

x²+x - 6 =0

D=1² - 4*1*(-6) = 1+24 = 25 = 5²

x1= (-1-5)/ (2*1) = -6/2 =-3

x2= (-1+5)/2 = 4/2=2

Пошаговое объяснение:

Answer 2

To solve the equation 3(x^2 + 1/x^2) + 5(x + 1/x) = 16, we first need to simplify the expression and then find the values of x that satisfy the equation. Let's proceed step by step:

Step 1: Simplify the expression To simplify the expression, we need to work on the terms with x^2 and x. To eliminate the fraction with x^2, we can multiply the entire equation by x^2:

x^2 * [3(x^2 + 1/x^2) + 5(x + 1/x)] = x^2 * 16

Step 2: Distribute and simplify Using the distributive property, we expand both sides of the equation:

3(x^4 + 1) + 5(x^3 + x) = 16x^2

Step 3: Expand further Multiply 3 to each term inside the brackets:

3x^4 + 3 + 5(x^3 + x) = 16x^2

Step 4: Distribute again Multiply 5 to each term inside the second set of brackets:

3x^4 + 3 + 5x^3 + 5x = 16x^2

Step 5: Move all terms to one side to set the equation to zero:

3x^4 + 5x^3 + 5x - 16x^2 + 3 = 0

Now, we have a quartic equation (an equation with a highest power of x^4). Unfortunately, there is no general algebraic formula to solve quartic equations like there is for linear and quadratic equations.

To find the solutions, you can use numerical methods or calculators to approximate the roots. If you have access to graphing tools or a graphing calculator, you can plot the graph of y = 3x^4 + 5x^3 + 5x - 16x^2 + 3 and find the x-values where the graph intersects the x-axis (y = 0). These points will be the solutions to the equation.

Keep in mind that quartic equations can have multiple solutions (real and/or complex), so you might find more than one value of x that satisfies the equation.