How many natural numbers between the following pairs?

Question

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How many natural numbers lie between the following pairs of numbers (100 square and 101 square) , (90 square and 91 square ) , (1000 square 1001 square )

200

180

2000

Step-by-step explanation:

a^2-b^2 = (a+b)(a-b)

101^2 -100^2-1

= (101+100*(101-100)-1

= 201*1 -1

= 200

91^2-90^2 -1

=(91+90)(91-90)-1

=181*1 -1

=180

1001^2-1000^2 -1

= (1001+1000)*(1001-1000) -1

= 2001*1 -1

= 2000

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: