J's answer to Alicia's Secondary 3 A Maths Singapore question.
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Alternatively,
x √50 = x√48 + √2
x(√50 - √48) = √2
Multiply both sides by (√50 + √48),
x(√50 - √48)(√50 + √48) = √2(√50 + √48)
x((√50)² - (√48)²) = √(2×50) + √2(√2√24)
x(50 - 48) = √100 + 2√24
2x = 10 + 2√24
x = 5 + √24
Second alternative :
x √50 = x√48 + √2
Multiply both sides by √2,
x√50√2 = x√48√2 + √2√2
x√100 = x(√24√2√2) + 2
10x = 2√24 x + 2
5x = √24x + 1
x(5 - √24) = 1
x(5-√24)(5 + √24) = 5 + √24
x(5² - (√24)²) = 5 + √24
x = 5 + √24
x √50 = x√48 + √2
x(√50 - √48) = √2
Multiply both sides by (√50 + √48),
x(√50 - √48)(√50 + √48) = √2(√50 + √48)
x((√50)² - (√48)²) = √(2×50) + √2(√2√24)
x(50 - 48) = √100 + 2√24
2x = 10 + 2√24
x = 5 + √24
Second alternative :
x √50 = x√48 + √2
Multiply both sides by √2,
x√50√2 = x√48√2 + √2√2
x√100 = x(√24√2√2) + 2
10x = 2√24 x + 2
5x = √24x + 1
x(5 - √24) = 1
x(5-√24)(5 + √24) = 5 + √24
x(5² - (√24)²) = 5 + √24
x = 5 + √24
Date Posted:
2 years ago
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