Mes. monthly
(Chp.3)
(40) The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find
the two numbers.
​

The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

Let the larger number be x

And, the square of the smaller number be 8x

x² − 8x = 180

⇒ x² − 8x − 180 = 0

⇒ x² − (18 − 10)x − 180 = 0

⇒ x² − 18x + 10x − 180 = 0

⇒ x (x − 18) + 10(x − 18) = 0

⇒ (x − 18) (x + 10) = 0

⇒ x − 18 = 0, x + 10 = 0

⇒ x = 18, x = −10

⇒ x = −10, 18

Either, x = −10 and x = 18

x = 18 (Positive value)

Now, the square of the smaller number = 8x = 8 × 18 = 144

So, the square of the smaller number = = 12

2fe + 3h2so4 -> fe2(so4)3 + 3h2

it is necessary to balance equations in order to get the proper amount of reactants as well as products in order not to make a miscalculation.

you cannot change the subscripts as that would change the substance itself. for instance, diatomic elements such as h2 only have the subscript two when a gas. another example would be so4, if you were to change the subscript, the element would no longer be sulfate.

we change the coefficients instead as that only changes the number of molecules rather than the substance itself.

hope this !

3 1/4 %

explanation: