If $${x^2} + \frac{1}{{{x^2}}} = \frac{7}{4}$$ for x > 0 then what is the value of $${x^4} + \frac{1}{{{x^4}}}.$$
A. $$1$$
B. $$\frac{{17}}{{16}}$$
C. $$\frac{{15}}{{16}}$$
D. $$\frac{{51}}{{16}}$$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Given, }}{x^2} + \frac{1}{{{x^2}}} = \frac{7}{4} \cr & {\text{Squaring both sides, we get}} \cr & {x^4} + \frac{1}{{{x^4}}} + 2 = \frac{{49}}{{16}} \cr & {x^4} + \frac{1}{{{x^4}}} = \frac{{49}}{{16}} - 2 \cr & {x^4} + \frac{1}{{{x^4}}} = \frac{{49 - 32}}{{16}} \cr & {x^4} + \frac{1}{{{x^4}}} = \frac{{17}}{{16}} \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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