Question

Решить уравнение: (9x² + 18x + 8)(49x² – 42x + 8)=341x²

Answer 1

Ответ:

Решение : ////////////////////////////////

Answer 2

To solve the equation (9x² + 18x + 8)(49x² – 42x + 8) = 341x², we need to first expand the left-hand side (LHS) and then simplify the equation to find the roots (values of x) that satisfy it.

Step 1: Expand the left-hand side (LHS) of the equation: (9x² + 18x + 8)(49x² – 42x + 8) = 341x²

To expand the LHS, we will use the distributive property of multiplication: LHS = 9x² * 49x² + 9x² * (-42x) + 9x² * 8 + 18x * 49x² + 18x * (-42x) + 18x * 8 + 8 * 49x² + 8 * (-42x) + 8 * 8

Simplify each term: LHS = 441x^4 - 378x³ + 72x² + 882x³ - 756x² + 144x + 392x² - 336x + 64

Now, combine like terms: LHS = 441x^4 + (882x³ - 378x³) + (72x² - 756x² + 392x²) + (144x - 336x) + 64

LHS = 441x^4 + 504x³ - 292x² - 192x + 64

Now, the equation becomes: 441x^4 + 504x³ - 292x² - 192x + 64 = 341x²

Step 2: Move all terms to one side of the equation: 441x^4 + 504x³ - 292x² - 192x + 64 - 341x² = 0

Step 3: Combine like terms: 441x^4 + 504x³ - 633x² - 192x + 64 = 0

Now, we have a quartic equation, which is an equation of the form ax^4 + bx³ + cx² + dx + e = 0.

Quartic equations are generally challenging to solve algebraically. However, we can attempt to find approximate solutions using numerical methods or graphing tools.

Using numerical methods, we can find approximate solutions. You can use numerical tools like the Newton-Raphson method or use graphing tools like graphing calculators or software to find the solutions.

Keep in mind that there may be multiple real and/or complex solutions to the equation.