Question

the sum of two numbers is 62 and their product is 960. the sum of their reciprocals is

Answer 1

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ANSWER:

• The sum of their reciprocals is 1/15 (or) 0.067

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ASSUMPTIOM:

• Take the numbers as x and y

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GIVEN:

• x + y = 62

• xy = 960

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TO FIND:

• 1/x + 1/y

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EXPLANATION:

METHOD 1:

x = 62 - y

Substitute x = 62 - y in xy = 960

(62 - y)y = 960

62y - y² = 960

y² - 62y + 960 = 0

By splitting the middle term.

y² - 32y - 30y + 960 = 0

y(y - 32) - 30(y - 32) = 0

Take (y - 32) as common

(y - 32) (y - 30) = 0

y = 32 (or) y = 30

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Substitute y = 32 in x = 62 - y

x = 62 - 32

x = 30

x = 62 - 30

x = 32

Hence the two numbers are 32 and 30

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Let us take x = 32 and y = 30

Substitute these values in 1/x + 1/y

1/x + 1/y = 1/32 + 1/30

1/32 + 1/30 = (32 + 30) ÷ (32 × 30)

1/32 + 1/30 = 64 / 960

1/32 + 1/30 = 1 / 15

1/32 + 1/30 = 0.2 / 3

1/32 + 1/30 = 0.066

1/x + 1/y = 1/32 + 1/30 = 0.067 (or) 1 / 15 .

HENCE SUM OF THEIR RECIPROCALS IS 0.067 (or) 1 / 15.

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METHOD 2:

1/x + 1/y = (x + y) / xy

Substitute x + y = 62 and xy = 960 in 1/x + 1/y = (x + y) / xy

1/x + 1/y = 62 / 960

1/x + 1/y = 1 / 15

1/x + 1/y = 0.067

HENCE SUM OF THEIR RECIPROCALS IS 0.067 (or) 1 / 15.

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NOTE : FOLLOW METHOD 1 ONLY WHEN VALUES x AND y ARE ASKED.

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