Number problems

Question

if 10>x>9 and x^2=(10-y)(10+y), which of the following is a possible value of y? 

A. -7

B. -6 

C. 3

D. 4

Answer 1

     y         (10-y)(10+y)                                   x

    ---      ----------------------------                   -----

A.  -7       (10-(-7))(10-7) = 17*3 = 51          √51 = 7.14

 

B.  -6       (10-(-6))(10-6) = 16*4 = 64          √64 = 8

 

C.   3       (10-3)(10+3) = 7*13 = 91          √91 = 9.54           9<x<10   YES !

 

D.  4       (10-4)(10+4) = 6*14 = 84          √84 = 9.17           9<x<10    YES !

 

 

Note that (10-y)(10+y) = 10 - y²

 

If x² = 10 - y²

    x² + y² = 10           [this is the equation of a circle or radius 10]

 

  so, the squares         100 - squares        square root of that:

A. -7     49                      51                            7.14

B. -6    36                       64                              8

C.  3     9                        91                             9.54

D.  4    18                       84                             9.17