Question

(a-1)^2 + (b-2)^2 + (c-3)^2 + (d-4)^4=0 find a×b×c×d×1=​

Answer 1

Answer:

W+X+Y+Z=0  

Now, if all of W, X, Y and Z are complete squares, which they are according to the question statement, and their sum is 0, we can be sure that all of them are 0s as well, or mathematically put,

W=0, X=0, Y=0, Z=0, if W+X+Y+Z=0 and W, X, Y and Z are perfect squares.

According to the given question,

W=(a−1)2; X=(b−2)2; Y=(c−3)2; Z=(d−4)2

Thus,

W=0⇒(a−1)2=0⇒a−1=0⇒a=1

X=0⇒(b−2)2=0⇒b−2=0⇒b=2

Y=0⇒(c−3)2=0⇒c−3=0⇒c=3

Z=0⇒(d−4)2=0⇒d−4=0⇒d=4

Thus, to answer the question, the value of the expression

abcd+1=1∗2∗3∗4+1=24+1=25

Hope that helped.