Question
Solve by factorizing this epwation y2_12y+11=0
Answers
GPT-4o mini
To solve the equation \( y^2 - 12y + 11 = 0 \) by factorizing, we need to find two numbers that multiply to 11 (the constant term) and add up to -12 (the coefficient of the linear term).
The pair of numbers that satisfy these conditions are -1 and -11. Thus, we can write:
\[
y^2 - 12y + 11 = (y - 1)(y - 11) = 0
\]
Now, we set each factor to zero:
1. \( y - 1 = 0 \)
\(\Rightarrow y = 1\)
2. \( y - 11 = 0 \)
\(\Rightarrow y = 11\)
Therefore, the solutions to the equation \( y^2 - 12y + 11 = 0 \) are:
\[
y = 1 \quad \text{and} \quad y = 11
\]
The pair of numbers that satisfy these conditions are -1 and -11. Thus, we can write:
\[
y^2 - 12y + 11 = (y - 1)(y - 11) = 0
\]
Now, we set each factor to zero:
1. \( y - 1 = 0 \)
\(\Rightarrow y = 1\)
2. \( y - 11 = 0 \)
\(\Rightarrow y = 11\)
Therefore, the solutions to the equation \( y^2 - 12y + 11 = 0 \) are:
\[
y = 1 \quad \text{and} \quad y = 11
\]