Mathematics: Find two numbers knowing that there’s some is 100 and the difference of their squares Is 1,000

Eight hundred and fifty million Two billion six hyndred and eighty...

Find two numbers knowing that there’s some is 100

Nelly6978

30.03.2021

the two numbers are 55 and 45

Step-by-step explanation:

let the numbers be x and y

according to the question :-

=》x + y = 100 - ( equation 1 )

and

=》

$x {}^{2} - {y}^{2} = 1000$

=》

(x + y)(x - y) = 1000

( by algebraic identity )

=》

$100 \times (x - y) = 1000$

=》

$(x - y) = 1000 \: \div100$

=》

(x - y) = 10

so,

by using linear equations :-

x + y = 100

x - y = 10

adding both equations we get,

=》2x = 110=》x = 110 / 2 =》x = 55

now, putting the value of x in equation 1

=》x + y = 100=》55 + y = 100=》y = 100 - 55 =》y = 45

i hope it helped you....

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