Question

if a and b are positive with a-b=2 and ab=24 then (1/a)+(1/b) is equal to

Answer 1

Step-by-step explanation:

Given :-

a-b = 2

ab = 24

To find :-

Find the value of (1/a)+(1/b)?

Solution :-

Given that

a-b = 2

ab = 24

We know that

(a+b)² = (a-b)² + 4ab

On Substituting these values in the above formula

=> (a+b)² = 2²+4(24)

=> (a+b)² = 4+96

=> (a+b)² = 100

=> a+b = ±√100

=> a+b = ±10

On taking positive value of a+b Since a and b are positive.

a+b = 10

Now the value of (1/a)+(1/b)

=>(b+a)/(ab)

=> (a+b)/(ab)

=> 10/24

=> 5/12

Therefore, (1/a)+(1/b) = 5/12

Answer:-

The value of (1/a)+(1/b) for the given problem is 5/12

Used formulae:-

• (a+b)² = (a-b)² + 4ab

Points to know:-

• (a+b)² = a²+2ab+b²

• (a-b)² = a²-2ab+b²

• (a-b)² = (a+b)²-4ab

• (a+b)²+(a-b)² = 2(a²+b²)

• (a+b)²-(a-b)² = 4ab

Answer 2

Step-by-step explanation:

Find the number of solutions of the equation 2x + y = 30 where both x and y are non-negative integers and x <= y.

Answer choices