58. Find x ÷ y, given that x^2 - y^2 = 10 and x - y = 2
(A) 3
(B) 5
(C) 7
(D) 9
Answers
Answer
7 / 3
Step-by-step explanation:
Given---> x² - y² = 10 and x - y = 2
To find---> find x ÷ y
Solution---> ATQ,
x - y = 2 ........................(1)
x² - y² = 10
We have an identity as follows,
a² - b² = ( a + b ) ( a - b ) , applying it here, we get,
=> ( x + y ) ( x - y ) = 10
Putting x - y = 2 , we get
=> ( x + y ) ( 2 ) = 10
=> x + y = 10 / 2
=> x + y = 5
=> y = 5 - x
Putting y = 5 - x in equation ( 1 )
=> x - ( 5 - x ) = 2
=> x - 5 + x = 2
=> 2x = 2 + 5
=> 2x = 7
=> x = 7 / 2
Putting x = 7 / 2 in y = 5 - x
=> y = 5 - x
=> y = 5 - ( 7 / 2 )
=> y = ( 10 - 7 ) / 2
=> y = 3 / 2
Now x ÷ y = ( 7 / 2 ) ÷ ( 3 / 2 )
= ( 7 / 2) × ( 2 / 3 )
= 7 / 3
7/3
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