Find the value of X and Y (X और Y का मान ज्ञात कीजिए)
I. `x^(2)-14x+48=0`
II. `y^(2)+6=5y`

Options

A. `xgty`
B. `ygtx`
C. x=y
D. none of these(इनमें से कोई नहीं)

Answer

To solve the equations given in the question, we will tackle each equation one by one.

### Step 1: Solve the first equation \(x^2 - 14x + 48 = 0\)

1. **Identify the coefficients**: Here, \(a = 1\), \(b = -14\), and \(c = 48\).
2. **Factor the quadratic equation**: We need to find two numbers that multiply to \(c\) (48) and add to \(b\) (-14). The numbers are -6 and -8.
- This gives us:
\[ (x - 6)(x - 8) = 0 \]
3. **Set each factor to zero**:
- \(x - 6 = 0 \Rightarrow x = 6\)
- \(x - 8 = 0 \Rightarrow x = 8\)

Thus, the values of \(x\) are \(6\) and \(8\).

### Step 2: Solve the second equation \(y^2 + 6 = 5y\)

1. **Rearrange the equation**: Move all terms to one side to set the equation to zero:
\[ y^2 - 5y + 6 = 0 \]
2. **Factor the quadratic equation**: We need to find two numbers that multiply to \(c\) (6) and add to \(b\) (-5). The numbers are -2 and -3.
- This gives us:
\[ (y - 2)(y - 3) = 0 \]
3. **Set each factor to zero**:
- \(y - 2 = 0 \Rightarrow y = 2\)
- \(y - 3 = 0 \Rightarrow y = 3\)

Thus, the values of \(y\) are \(2\) and \(3\).

### Final Answer:
The values of \(x\) are \(6\) and \(8\), and the values of \(y\) are \(2\) and \(3\).

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