The sum of two integers is -11 and their product is -80. What are the two integers?icta science experiment, it is required to decrease the temperature from 36°C att
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Answer:
The sum of two integers is -11 and their product is -80. What are the two integers?<br />icta science experiment, it is required to decrease the temperature from 36°C attempt
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Answer :
x = 5 , - 16.
y = 5 , - 16.
Solution :
Let, The two integers be x and y.
★ Case 1.
The sum of two integers is -11.
→ x + y = - 11. _________ ( 1 )
★ Case 2.
their product is -80.
→ x * y = - 80.________ ( 2 )
Now, Taking Equation ( 2 )
→ x * y = - 80.
→ y = - 80 / x. _______ ( 3 )
Putting the value of y in Equation ( 1 )
→ x + y = - 11.
→ x - 80 / x = - 11.
→ x² - 80 = - 11x.
→ x² + 11x - 80 = 0.
→ x² + 16x - 5x - 80 = 0.
→ x( x + 16 ) - 5( x + 16 ) = 0.
→ ( x - 5 )( x + 16 ) = 0.
Either,
→ x - 5 = 0.
→ x = 5.
Or,
→ x + 16 = 0.
→ x = - 16.
Now, Putting the value of x in Equation ( 3 )
→ y = - 80/ x
→ y = 80 / 16
→ y = 5.
Or,
→ y = - 80 / 5
→ y = - 16.
Therefore, the value of x is 5 , - 16 and y = 5, - 16.
Verification :
When,
x = 5.
y = - 16.
→ x + y = - 11.
→ 5 - 16 = - 11.
When,
x = - 16.
y = 5.
→ x + y = - 11.
→ - 16 + 5 = - 11.
Taking Equation ( 2 )
When,
x = 5.
y = 16.
→ x * y = - 80.
→ 5 * - 16 = - 80.
When,
x = - 16
y = 5.
→ x * y = - 80.
→ - 16 * 5 = - 80.
Hence Verify