If \frac{a^2}{b^2 + c^2} = \frac{b^2}{c^2 + a^2} = \frac{c^2}{a^2 + b^2}, then what is the value of a^4 + b^4 + c^4 equal to ?
- A. a^2b^2 + b^2c^2 + c^2a^2 ✓
- B. 2(a^2b^2 + b^2c^2 + c^2a^2)
- C. 3(a^2b^2 + b^2c^2 + c^2a^2)
- D. 4(a^2b^2 + b^2c^2 + c^2a^2)
Correct Answer: A. a^2b^2 + b^2c^2 + c^2a^2
Explanation
By symmetry, setting a=b=c=1 satisfies the given equation (ratios equal 1/2). Substituting these values into a^4+b^4+c^4 yields 3. Only option (a) equals 3 when evaluated with a=b=c=1.
Related questions on Algebra
- If p + q + r = 0, then what is z^{\frac{p^2}{qr}} \times z^{\frac{q^2}{rp}} \times z^{\frac{r^2}{pq}} equal to ?
- What is the value of k for which (k^2 - 5k + 4)x^2 + (k^2 - 3k - 4)x + (k^2 - 4k) = 0 is an identity ?
- If \frac{1}{x} = \frac{1}{p} + \frac{1}{q}, then what is \frac{pq}{p^2 - q^2}\left(\frac{x + p}{x - p} - \frac{x + q}{x - q}\right) equa...
- If (x - 5) is the HCF of x^2 - x - p and x^2 - qx - 10, then what is the value of (p + q) ?
- Which one of the following is a factor of the polynomial (x-1)(x-2)(x-4)-90?