Question

The number of elements in the set A={(a,b): 2 a square + 3 b square equals to 35,a,b€z} where z is the set of all integers

Answer 1

Given:

set A={(a,b): 2 a² + 3 b² = 35  ,  a, b € z

Z is the set of all integers.

To Find:

The number of elements in A.

Solution:

• We have 2a² + 3b²  = 35

• We can see that 2a² > 0

Therefore,

• 3b² < 35
• b² <35/3
• b² < 11
• b² = { 1 , 4, 9}

Similarly,

• 2a² < 35
• a² < 35/2
• a² = { 1, 4, 9, 16 }

Let a² = 1

• 3b² = 33
• b² = 11 , not possible

Let a² = 4

• 3b² = 27
• b² = 9, possible
• Possible solutions: (2,3) , (-2,3) , (-2,-3) and (2,-3)

Let a² = 9

• 3b² = 17 , not possible

Let a² = 16

• 3b² = 3
• b² = 1
• Possible solutions : (4,1) , (4,-1) , (-4,-1) and (-4,1)

The number of elements in the set A={(a,b): 2 a square + 3 b square equals to 35,a,b€z} is 8.

Answer 2

Answer:

8 answer

(-2,3)(2,3)

Step-by-step explanation:

(-1,2)(2,4)