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secondary 3 | A Maths
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Hello! Can anyone help me with this question!
Date Posted: 2 years ago
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done
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clear
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Rough idea, but we have to be careful at the last part because the coefficient in front of the square root at the end has to be exactly 1.
Date Posted:
2 years ago
Might be easier to simplify the √ first.
I looked at it for a while before deciding to not simplify first.
Because 50 - 48 = 2.
Because 50 - 48 = 2.
For us, easy to spot that.
For students, big surds might be difficult to process. So probably breaking it down might help.
Anyway, Alicia, I've uploaded my workings.
For students, big surds might be difficult to process. So probably breaking it down might help.
Anyway, Alicia, I've uploaded my workings.
Thank you so much!
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
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
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