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if x= root3+1 upon root3-1 y=root3-1 upon root3+1 find the value of x2+xy-y2
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if x= root3+1 upon root3-1 y=root3-1 upon root3+1 find the value of x2...
Given: x = √3 / (√3 - 1), y = (√3 - 1) / √3
To find: x²xy - y²
Solution:
Step 1: Simplify x and y
x = √3 / (√3 - 1) * (√3 + 1) / (√3 + 1) = (√3 + 1) / 2
y = (√3 - 1) / √3 * (√3 + 1) / (√3 + 1) = (√3 - 1) / 2
Step 2: Find x² and y²
x² = (√3 + 1)² / 4 = (4 + 2√3) / 4 = 1 + √3 / 2
y² = (√3 - 1)² / 4 = (4 - 2√3) / 4 = 1 - √3 / 2
Step 3: Substitute the values of x, y, x² and y² in the expression x²xy - y²
x²xy - y² = [(1 + √3 / 2)(√3 + 1) / 2][(√3 + 1) / 2] - (1 - √3 / 2)
= [(√3 + 1)(√3 + 1)] / 4 - (1 - √3 / 2)
= (4 + 2√3) / 4 - (2 - √3) / 2
= (2 + √3) / 2 - (2 - √3) / 2
= √3
Answer: x²xy - y² = √3.
To find: x²xy - y²
Solution:
Step 1: Simplify x and y
x = √3 / (√3 - 1) * (√3 + 1) / (√3 + 1) = (√3 + 1) / 2
y = (√3 - 1) / √3 * (√3 + 1) / (√3 + 1) = (√3 - 1) / 2
Step 2: Find x² and y²
x² = (√3 + 1)² / 4 = (4 + 2√3) / 4 = 1 + √3 / 2
y² = (√3 - 1)² / 4 = (4 - 2√3) / 4 = 1 - √3 / 2
Step 3: Substitute the values of x, y, x² and y² in the expression x²xy - y²
x²xy - y² = [(1 + √3 / 2)(√3 + 1) / 2][(√3 + 1) / 2] - (1 - √3 / 2)
= [(√3 + 1)(√3 + 1)] / 4 - (1 - √3 / 2)
= (4 + 2√3) / 4 - (2 - √3) / 2
= (2 + √3) / 2 - (2 - √3) / 2
= √3
Answer: x²xy - y² = √3.
Community Answer
if x= root3+1 upon root3-1 y=root3-1 upon root3+1 find the value of x2...
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