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Sagot :
To find the value of [tex]\( t \)[/tex] given the equation
[tex]\[ k = \frac{a^2 + t}{2 - a} \][/tex]
where [tex]\( a = 4 \)[/tex] and [tex]\( k = -11 \)[/tex], we will follow these steps:
1. Substitute the given values into the equation:
[tex]\[ -11 = \frac{4^2 + t}{2 - 4} \][/tex]
2. Evaluate the expressions inside the fraction:
[tex]\[ -11 = \frac{16 + t}{-2} \][/tex]
3. Simplify the right-hand side of the equation:
[tex]\[ -11 = \frac{16 + t}{-2} \][/tex]
To eliminate the fraction, multiply both sides of the equation by -2:
[tex]\[ (-11) \times (-2) = 16 + t \][/tex]
[tex]\[ 22 = 16 + t \][/tex]
4. Solve for [tex]\( t \)[/tex]:
Subtract 16 from both sides of the equation:
[tex]\[ t = 22 - 16 \][/tex]
[tex]\[ t = 6 \][/tex]
Therefore, the value of [tex]\( t \)[/tex] is:
[tex]\[ \boxed{6} \][/tex]
[tex]\[ k = \frac{a^2 + t}{2 - a} \][/tex]
where [tex]\( a = 4 \)[/tex] and [tex]\( k = -11 \)[/tex], we will follow these steps:
1. Substitute the given values into the equation:
[tex]\[ -11 = \frac{4^2 + t}{2 - 4} \][/tex]
2. Evaluate the expressions inside the fraction:
[tex]\[ -11 = \frac{16 + t}{-2} \][/tex]
3. Simplify the right-hand side of the equation:
[tex]\[ -11 = \frac{16 + t}{-2} \][/tex]
To eliminate the fraction, multiply both sides of the equation by -2:
[tex]\[ (-11) \times (-2) = 16 + t \][/tex]
[tex]\[ 22 = 16 + t \][/tex]
4. Solve for [tex]\( t \)[/tex]:
Subtract 16 from both sides of the equation:
[tex]\[ t = 22 - 16 \][/tex]
[tex]\[ t = 6 \][/tex]
Therefore, the value of [tex]\( t \)[/tex] is:
[tex]\[ \boxed{6} \][/tex]
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