J's answer to Alicia's Secondary 3 A Maths Singapore question.
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x √50 = x√48 + √2
x √(25×2) = x√(16×3) + √2 (you can skip this step if you want)
x √25 √2 = x √16 √3 + √2
5√2 x = 4√3 x + √2
(5√2 x - 4√3) x = √2
Multiply both sides by (5√2 + 4√3),
(5√2 + 4√3)((5√2 + 4√3) x = √2(5√2 + 4√3),
((5√2)² - (4√3)²) x = 5 × 2 + 4√2√3
(50 - 48)x = 10 + 4√6
2x = 10 + 4√6
x = 5 + 2√6
x = 5 + √(6×2²) = 5 + √24
x √(25×2) = x√(16×3) + √2 (you can skip this step if you want)
x √25 √2 = x √16 √3 + √2
5√2 x = 4√3 x + √2
(5√2 x - 4√3) x = √2
Multiply both sides by (5√2 + 4√3),
(5√2 + 4√3)((5√2 + 4√3) x = √2(5√2 + 4√3),
((5√2)² - (4√3)²) x = 5 × 2 + 4√2√3
(50 - 48)x = 10 + 4√6
2x = 10 + 4√6
x = 5 + 2√6
x = 5 + √(6×2²) = 5 + √24
Date Posted:
2 years ago
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