Answers

2015-04-07T18:10:54+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let the number be  N =  a b    where  b is the units digit.  a = the tens digit.

the value of the number N = 10 * a + b
       number after reversing :  b a
the value of the number after reversing :  10 * b  + a

sum of the two numbers = 10 a + b + 10 b + a  = 11 (a + b)
   given,  11 ( a + b) = 143          =>  a + b = 13    --- (1)
   
   sum of squares of digits = a² + b²  = (a+b)² - 2 a b
   given,      N = 10 a + b  = (a² + b²) - 3
          =>   10 a + b =  (13² - 2 a b) - 3 =  166 - 2 a b
    Hence,  10 a + b + 2 a b =  166      --- (2)

  do  (2) - 10 * (1) :  - 9 b + 2 a b = 36
            so       b (2a -9) = 36    --- (4) .

     substitute value of b from (1) in (4) :
             (13 - a) ( 2a - 9) = 36
     =>   -2 a²  + 35 a - 117 = 36
       =>    2 a² - 35 a + 153 = 0
          discr:  35² - 8 * 153 = 1
             a = (35 +- 1)/ 4  =  9  or  8.5
  we take the integer value only as a and b are integers less than 10.
        so a = 9 and   b = 4

so the number is  94.

1 5 1
Sir very good ! You are really a genius
yes sir
2015-04-07T19:14:35+05:30
Let the tens digit of the no. be 'x'. and ones digit be 'y'
the no. will be 10x+y
according to the question,,10x+y + 10y+x=143
                                       11x+11y=143
by solving we get             x+y=13
                                       y=x-13   ..............eq 1
 
  according to the question,,10x+y+3=x²+y² ............................eq 2
  substituting eq 1 in eq 2
                                        10x+13-x+3=x²+(13-x)²
 by solving we get              2x²-35x+153=0
 
Solving the quadratic equation
a=2          b=-35             c=153
determinant=b²-4ac
                 =1225-1224
                 =1
          √D   =1

x=-b+√D÷2a                               or        x=-b-√D÷2a
x=9                                           or        x=34/4(ruled out since digits cannot 
                                                                        be fractions)
hence   x=9
            y=13-9
             =4
the number is 94.

hope this helps u...
0