Question 58

If $$A = \frac{3 \times 4 + 2}{6 \div 3 + 2}$$ and $$B = \frac{12 \div 6 \times 2}{8 \div 4 - 3}$$, then what is the value of $$A^2 + B^2 - 2AB$$?

Solution

$$A = \frac{3 \times 4 + 2}{6 \div 3 + 2}$$

$$A=\frac{12+2}{2+2}$$

$$A=\frac{14}{4}$$

A = 3.5

$$B = \frac{12 \div 6 \times 2}{8 \div 4 - 3}$$

$$B=\frac{\frac{12}{6}\times2}{\frac{8}{4}-3}$$

$$B=\frac{2\times2}{2-3}$$

B = -4

Value of $$A^2 + B^2 - 2AB$$ = $$\left(A-B\right)^2$$

= $$(3.5-(-4))^2$$

= $$(3.5+4)^2$$

= $$(7.5)^2$$

= 56.25


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