Question : If $a^2+b^2+1=2 a$, then the value of $a^4+b^7$ is:
Option 1: 1
Option 2: 0
Option 3: 2
Option 4: 4
Answer (1)
21st Jan, 2024
Correct Answer: 1
Solution :
Given: $a^2+b^2+1=2 a$
⇒ $a^2+b^2+1-2a=0$
⇒ $a^2+1-2a+b^2=0$
⇒ $(a-1)^2+b^2=0$
If the sum of the squares of two numbers is zero then both the numbers are zero.
So, $(a-1)=0$ and $b=0$
$\therefore a=1,b=0$
Putting the values, we get
$a^4+b^7=1+0=1$
Hence, the correct answer is 1.
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