If a + b = 10 and $$\sqrt {\frac{a}{b}} - 13 = - \sqrt {\frac{b}{a}} - 11$$ then what is the value of 3ab + 4a2 + 5b2?
A. 450
B. 300
C. 600
D. 750
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let }}\sqrt {\frac{a}{b}} = x \cr & \therefore \,x - 13 = \frac{{ - 1}}{x} - 11 \cr & x + \frac{1}{x} = 2 \cr & \therefore \,x = 1 \cr & \sqrt {\frac{a}{b}} = 1{\text{ and }}a + b = 10 \cr & \therefore \,a = b = 5 \cr & 3ab + 4{a^2} + 5{b^2} \cr & = 3{a^2} + 4{a^2} + 5{a^2} \cr & = 12{a^2} \cr & = 12 \times 25 \cr & = 300 \cr} $$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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