Question

the product of 3 consecutive integers is 120 then the greatest number is​

Answer 1

Answer :-

The Greatest Number = 6.

Explanation :-

Given :

• The product of 3 consecutive integers is 120.

To Find :

• The Greatest Number.

Solution :

Here, Consecutive Numbers means Repeating Numbers.

Example :- 1,2,3 etc.

Let,

• 1st Number = x - 1.
• 2nd Number = x.
• 3rd Number = x + 1.

According to the Question,

➙ (x - 1)(x)(x + 1) = 120.

➙ (x² - 1²)(x) = 120.

➙ x³ - x = 120.

➙ x³ - x - 120 = 0.

To find the value of x, we will use Trial and Error method.

Let's Assume x = 1.

➙ (1)³ - 1 - 120 = 0.

➙ -120 = 0.

LHS is not equal to RHS.

Let's Assume x = 5.

➙ (5)³ - 5 - 120 = 0.

➙ 125 - 5 - 120 = 0.

➙ 120 - 120 = 0.

➙ 0 = 0.

So, x = 5.

Therefore,

• 1st Number = x - 1 = 4.
• 2nd Number = x = 5.
• 3rd Number = x + 1 = 6.

We have to find the greatest number.

So, The Greatest Number = 6.

Answer 2

Question :

The product of 3 consecutive integers is 120 then find the greatest number.

Given :

• Product of 3 consecutive integers = 120

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To find :

• The greatest number.

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Solution :

Let the first integer = x

Let second integer = x + 1

Let third integer = x + 2

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According to the question :

(x) × (x + 1 )× (x + 2) = 120

↦ (x² + x )(x + 2) = 120

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↦ x³ + 2x² + x² + 2x = 120

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↦ x³ + 3x² + 2x - 120 = 0

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↦ (x - 4) (x² + 7x + 30 ) = 0

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↦ x = 4 (for x be integer we must have x=4)

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↦ First number = x = 4

↦ Second number = x + 1 = 4 + 1 = 5

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↦ Third number = x + 2 = 4 + 2 = 6

Therefore, the greatest number = 6.