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secondary 3 | A Maths
2 Answers Below
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Date Posted: 4 years ago
Views: 222
(a)
2²ˣ⁻⁴ x 40 = 5²⁻ˣ
=> 4ˣ x 2⁻⁴ x 40 = 5² x 5⁻ˣ
=> 4ˣ x 1/16 x 40 = 25 x 1/5ˣ
=> 4ˣ x 1/2 = 5 x 1/5ˣ
=> 4ˣ = 10 x 1/5ˣ
=> 4ˣ x 5ˣ = 10
=> (4 x 5)ˣ = 10
=> 20ˣ = 10
(b)
5ˣ⁻¹ + 5²⁻ˣ = 6
=> 5ˣ/5 + 25/5ˣ = 6
subst. u = 5ˣ ;
=> u/5 + 25/u = 6
=> u² + 125 = 30u
=> u² - 30u + 125 = 0
=> (u - 5)(u - 25) = 0
=> u = 5 or u = 25
=> 5ˣ = 5¹ or 5ˣ = 5²
=> x = 1 or x = 2
...
2²ˣ⁻⁴ x 40 = 5²⁻ˣ
=> 4ˣ x 2⁻⁴ x 40 = 5² x 5⁻ˣ
=> 4ˣ x 1/16 x 40 = 25 x 1/5ˣ
=> 4ˣ x 1/2 = 5 x 1/5ˣ
=> 4ˣ = 10 x 1/5ˣ
=> 4ˣ x 5ˣ = 10
=> (4 x 5)ˣ = 10
=> 20ˣ = 10
(b)
5ˣ⁻¹ + 5²⁻ˣ = 6
=> 5ˣ/5 + 25/5ˣ = 6
subst. u = 5ˣ ;
=> u/5 + 25/u = 6
=> u² + 125 = 30u
=> u² - 30u + 125 = 0
=> (u - 5)(u - 25) = 0
=> u = 5 or u = 25
=> 5ˣ = 5¹ or 5ˣ = 5²
=> x = 1 or x = 2
...
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First part
Date Posted:
4 years ago
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Date Posted:
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