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s irrational answers 6. r^(2)-8r+8=0

s irrational answers\newline66. r2−8r+8=0 r^{2}-8 r+8=0

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Q. s irrational answers\newline66. r2−8r+8=0 r^{2}-8 r+8=0
  1. Identify type and method: Step 11: Identify the type of equation and decide the method to solve it.\newlineWe have a quadratic equation r2−8r+8=0 r^2 - 8r + 8 = 0 . We'll use the quadratic formula r=−b±b2−4ac2a r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} .
  2. Apply quadratic formula: Step 22: Apply the quadratic formula.\newlineHere, a=1 a = 1 , b=−8 b = -8 , and c=8 c = 8 .\newlineCalculate the discriminant Δ=b2−4ac \Delta = b^2 - 4ac .\newlineΔ=(−8)2−4⋅1⋅8=64−32=32 \Delta = (-8)^2 - 4 \cdot 1 \cdot 8 = 64 - 32 = 32 .
  3. Check discriminant and calculate: Step 33: Since the discriminant is positive and not a perfect square, the solutions are irrational.\newlineCalculate r r using the quadratic formula:\newliner=−(−8)±322⋅1=8±322 r = \frac{-(-8) \pm \sqrt{32}}{2 \cdot 1} = \frac{8 \pm \sqrt{32}}{2} .
  4. Simplify the solutions: Step 44: Simplify the solutions.\newline32=16⋅2=42 \sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2} ,\newlineSo, r=8±422=4±22 r = \frac{8 \pm 4\sqrt{2}}{2} = 4 \pm 2\sqrt{2} .

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