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Sagot :
Answer:
k = ±2√5 + 3
Step-by-step explanation:
- k² - 6k + 9 = 11 + 9
- (k - 3)² = 20
- k - 3 = √20
- k - 3 = ±2√5
- k = ±2√5 + 3
Answer:
[tex]k=3+2\sqrt5\ or\ k=3-2\sqrt5[/tex]
Step-by-step explanation:
[tex]k^2-6k=11[/tex]
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Add one term in order to complete the square
[tex]k^2-6k+(6\times\frac{1}{2})^2=11+(6\times\frac{1}{2})^2[/tex]
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Calculate
[tex]k^2-6k+3^2=11+3^2[/tex]
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Factor the expression using [tex]a^2\pm 2ab+b^2=(a\pm b)^2[/tex]
[tex](k-3)^2=11+3^2[/tex]
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Calculate the power
[tex](k-3)^2=11+9[/tex]
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Calculate the sum or difference
[tex](k-3)^2=20[/tex]
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Split into two equations
[tex]k-3=\sqrt{20}\ or\ k-3=-\sqrt{20}[/tex]
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Move variables to the left side of the equation:
[tex](k-3=\sqrt{20})[/tex]
[tex]k=\sqrt{20}+3\\ k=2\sqrt{5}+3[/tex]
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Move variables to the left side of the equation:
[tex](k-3=-\sqrt{20})[/tex]
[tex]k=\sqrt{20}+3\\ k=-2\sqrt{5}+3[/tex]
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So far:
[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]
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Find the union of the solutions
[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]
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I hope this helps you
:)
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