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the difference of the squares of two numbers is 160. the square of the smaller number is 6 times larger number. ​

Sagot :

Bloom018idn

12

Step-by-step explanation:

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.

Answer

We have,

Let the large number is =x

Square of smaller number is =8x

Now, According to given question,

x^2 −8x=180

⇒x^2 −8x−180=0

⇒x^2 −(18−10)x−180=0

⇒x^2−18x+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 is true (Positive value)

Now, square of small number

=18x=18×8=144

144

=12