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secondary 2 | Maths
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TIA!
Date Posted: 2 years ago
Views: 329
One idea is as follows.
k² - 3k + 5 = 0
k² - 3k = -5
Squaring both sides,
(k² - 3k)² = (-5)²
(k² - 3k)² = 25
We can do rainbow expansion on (k² - 3k)² or some other suitable approach, unless you can expand it mentally in your head!
k⁴ - 3k³ - 3k³ + 9k² = 25
k⁴ - 6k³ + 9k² = 25
All we need to do is to subtract both sides by 7.
k⁴ - 6k³ + 9k² - 7 = 25 - 7
k⁴ - 6k³ + 9k² - 7 = 18
So the value of k⁴ - 6k³ + 9k² - 7 is 18.
k² - 3k + 5 = 0
k² - 3k = -5
Squaring both sides,
(k² - 3k)² = (-5)²
(k² - 3k)² = 25
We can do rainbow expansion on (k² - 3k)² or some other suitable approach, unless you can expand it mentally in your head!
k⁴ - 3k³ - 3k³ + 9k² = 25
k⁴ - 6k³ + 9k² = 25
All we need to do is to subtract both sides by 7.
k⁴ - 6k³ + 9k² - 7 = 25 - 7
k⁴ - 6k³ + 9k² - 7 = 18
So the value of k⁴ - 6k³ + 9k² - 7 is 18.
Thx so much Eric Nicholas K!
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