दोन क्रमागत सम संख्याचा लसावि 90 आहे तर त्या संख्या कोणत्या ?
Answers
Solution :-
Let us assume that the two consecutive even numbers are 2x and (2x + 2)
we know that,
- First number * Second number Product = HCF * LCM
- HCF of two even numbers = 2
then,
→ 2x * (2x + 2) = 2 * 90
→ 2x² + 2x = 90
→ 2(x² + x) = 90
→ x² + x - 45 = 0
solving,
→ x = (- 1 ± √181)/2
given data is incorrect .
Correct Question :- Find two consecutive even numbers have LCM as 180 ?
Solution :-
Let us assume that the two consecutive even numbers are 2x and (2x + 2)
→ 2x * (2x + 2) = 2 * 180
→ 2x² + 2x = 180
→ 2(x² + x) = 180
→ x² + x - 90 = 0
→ x² + 10x - 9x - 90 = 0
→ x(x + 10) - 9(x + 10) = 0
→ (x + 10)(x - 9) = 0
→ x = (-10) or 9
taking positive value now,
therefore,
→ First number = 2 * 9 = 18
→ Second number = (2 * 9 + 2) = 20
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