positivenumber is represented by 10t + usum of the squares of the digits is 26the number is decreased by number its digits reversed the result is 36Findnumber

Question

the answer is either 51, 26, 38 or 67

Answer 1

 

10t+u is the number

t²+u²=26

(10t+u)-(10u+t)=36

10t+u-10u-t=36

9t-9u=36

divide both sides by 9

t-u=4

t=u+4

t²+u²=26

(u+4)²+u²=26

u²+8u+16+u²=26

2u²+8u+16=26

2u²+8u+16-26=0

2u²+8u-10=0

divide both sides by 2

u²+4u-5=0

factor

(u+5)(u-1)=0

u-1=0

u=1

t²+1²=26

t²=26-1

t²=25

t=5

the number is 51

note: this is the correct algebraic way to solve the problem and this is the way that you should solve the problem; however, looking at t²+u²=26, how many perfect squares are there less than 26 ?

1,4,9,16, and 25-which of these two add up to 26 ?