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secondary 3 | A Maths
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Dunelm
Dunelm

secondary 3 chevron_right A Maths chevron_right Singapore

Need help for this question. Thank You

Date Posted: 2 years ago
Views: 148
J
J
2 years ago
Sum is 2.

h + k + 2k = 2
h + 3k = 2

We take it as h and k are different.


The equation tells This tells you that some of those integers are non-positive

(If not , h + 3k would be bigger than 2. Eg. If k = 1 and h = 2)
J
J
2 years ago
Sum of squares = 30

h² + k² + (2k)² = 30

h² + k² + 4k² = 30

h² + 5k² = 30 ①


Since h + 3k = 2,

h = 2 - 3k

h² = (2 - 3k)²

h² = 4 - 12k + 9k² ②


Sub ② into ①,


4 - 12k + 9k² + 5k² = 30

14k² - 12k - 26 = 0

Divide both sides by 2,

7k² - 6k - 13 = 0

(7k - 13)(k + 1) = 0

7k = 13 or k = -1
k = -13/7
(Rejected as k is an integer)


So, k = -1 and 2k = -2

h = 2 - 3(1) = 5

Your integers are :

5 , -1 and -2

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PhysChemTutor
Physchemtutor's answer
1551 answers (A Helpful Person)
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Dunelm
Dunelm
2 years ago
Thank You.
J
J
2 years ago
Do take note that you'll need to show that k = -13/7 is rejected and also to give the reason why.
See question's main comments section for working and explanation.
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J
J's answer
1022 answers (A Helpful Person)