Konsep Dasar Aljabar

Hello everyone! Today we are looking at Algebra, specifically Algebraic Manipulation. If we are given the equation x squared minus three x plus one equals zero, we need to find the value of x squared plus one over x squared.

In step one, we divide the entire equation by x. Taking x squared minus three x plus one equals zero and dividing both sides by x where x is not zero, we get x squared over x minus three x over x plus one over x equals zero over x. This simplifies to x minus three plus one over x equals zero.

This means x plus one over x equals three. Now, for step two, we square both sides. Using the identity a plus b squared equals a squared plus two a b plus b squared, our equation x plus one over x squared equals three squared expands to x squared plus two times x times one over x plus one over x squared equals nine.

The middle term simplifies, leaving x squared plus two plus one over x squared equals nine. For the final step, we subtract two from both sides, so x squared plus one over x squared equals nine minus two. The final answer is seven.

In conclusion: first, change the equation form into x plus one over x. Second, apply the squaring identity. And third, simplify the expression to reach the final result.

Mastering these manipulations is key to solving algebra problems efficiently. See you in the next lesson!