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
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.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : If $x=(\sqrt[3]{7})^{3}+3$, then the value of $x^3–9x^2+27x–34$ is:
Question : If $x^2-7x+1=0$, what is the value of $(x+\frac{1}{x})$.
Question : If a3 + b3 = 217 and a + b = 7, then the value of ab is:
Question : If the sum of $\frac{a}{b}$ and its reciprocal is 1 and $a\neq 0,b\neq 0$, then the value of $a^{3}+b^{3}$ is:
Question : If $a^{2}+b^{2}+c^{2}=ab+bc+ca,$ then the value of $\frac{a+c}{b}$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile