Answer :
To solve the equation [tex]\( y^4 = 169 \)[/tex], you need to find the value of [tex]\( y \)[/tex] that makes the equation true.
Here are the steps to solve it:
1. Understand the equation: You have the equation [tex]\( y^4 = 169 \)[/tex]. This means any value of [tex]\( y \)[/tex] raised to the fourth power will equal 169.
2. Find the fourth root: To solve for [tex]\( y \)[/tex], you need to take the fourth root of both sides of the equation.
3. Consider both positive and negative roots: While taking the root, remember that both a positive and a negative number raised to an even power (like 4) will result in a positive number. Therefore, you should consider both:
[tex]\[
y = \sqrt[4]{169} \quad \text{and} \quad y = -\sqrt[4]{169}
\][/tex]
4. Calculate the fourth root of 169: After calculating, you find that [tex]\( \sqrt[4]{169} \approx 3.605551275463989 \)[/tex].
5. Write the solutions: There are two solutions for [tex]\( y \)[/tex]:
[tex]\[
y \approx 3.605551275463989
\][/tex]
and
[tex]\[
y \approx -3.605551275463989
\][/tex]
So, the solutions to the equation [tex]\( y^4 = 169 \)[/tex] are approximately [tex]\( y = 3.605551275463989 \)[/tex] and [tex]\( y = -3.605551275463989 \)[/tex].
Here are the steps to solve it:
1. Understand the equation: You have the equation [tex]\( y^4 = 169 \)[/tex]. This means any value of [tex]\( y \)[/tex] raised to the fourth power will equal 169.
2. Find the fourth root: To solve for [tex]\( y \)[/tex], you need to take the fourth root of both sides of the equation.
3. Consider both positive and negative roots: While taking the root, remember that both a positive and a negative number raised to an even power (like 4) will result in a positive number. Therefore, you should consider both:
[tex]\[
y = \sqrt[4]{169} \quad \text{and} \quad y = -\sqrt[4]{169}
\][/tex]
4. Calculate the fourth root of 169: After calculating, you find that [tex]\( \sqrt[4]{169} \approx 3.605551275463989 \)[/tex].
5. Write the solutions: There are two solutions for [tex]\( y \)[/tex]:
[tex]\[
y \approx 3.605551275463989
\][/tex]
and
[tex]\[
y \approx -3.605551275463989
\][/tex]
So, the solutions to the equation [tex]\( y^4 = 169 \)[/tex] are approximately [tex]\( y = 3.605551275463989 \)[/tex] and [tex]\( y = -3.605551275463989 \)[/tex].
