1.

The sum of three numbers in A.P is -3 and the product is 8 then find the three numbers

Answer»

GIVEN :-

Sum of THREE numbers in A.P is -3 and the product is 8.

  • S = -3
  • P = 8

TO FIND :-

The three numbers which are in A.P.

SOLUTION :-

LET the three numbers be a - d, a and a + d.

A/q,

S = a - d + a + a + d = -3

⇒a + a + a = -3

⇒3a = -3

⇒a = -3/3

⇒a = -1

\rule{110}<klux>2</klux>

Again,

P = a(a - d)(a + d) = 8

Putting the value of a :-

⇒ -1(-1 - d)(-1 + d) = 8

⇒ -1 × [ (-1)² - (d)²] = 8

⇒ -1 × (1 - d²) = 8

⇒ -1 + d² = 8

⇒ d² = 9

⇒d = √9

⇒d = ±3

\rule{110}2

CASE - 1 :-

If d = +3, the numbers are :-

  • a - d = -1 - 3 = -4
  • a = -1
  • a + d = -1 + 3 = 2

\rule{80}2

CASE - 2 :-

If d = -3, the numbers are :-

  • a - d = -1 - (-3) = -1 + 3 = 2
  • a = -1
  • a + d = -1 + (-3) = -1 - 3 = -4

Therefore, the numbers are 2, -1 and -4.


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