Given:$x^2 + \frac{1}{x^2} = 18$To do:We have to find the values of $x + \frac{1}{x}$ and $x - \frac{1}{x}$.Solution:The given expression is $x^2 + \frac{1}{x^2} = 18$. Here, we have to find the values of $x + \frac{1}{x}$ and $x - \frac{1}{x}$. So, by using the identities $(a+b)^2=a^2+2ab+b^2$...................(i) and $(a-b)^2=a^2-2ab+b^2$.............(ii), ... Read More

Given:(i) $4x = (52)^2 – (48)^2$  (ii) $14x = (47)^2 – (33)^2$  (iii) $5x = (50)^2 – (40)^2$To do:We have to find the value of $x$ in each case.Solution:Here, we have to find the value of $x$ in each expression. The given expressions are the difference of two squares. So, ... Read More

Given:(i) $(82)^2 – (18)^2$  (ii) $(467)^2 – (33)^2$  (iii) $(79)^2 – (69)^2$  (iv) $197 \times 203$  (v) $113 \times 87$  (vi) $95 \times 105$  (vii) $1.8 \times 2.2$  (viii) $9.8 \times 10.2$To do:We have to simplify the given expressions using the formula: $(a – b) (a + b) = a^2 ... Read More

Given:(i) $\frac{((58)^2 – (42)^2)}{16}$  (ii) $178 \times 178 – 22 \times 22$  (iii) $\frac{(198 \times 198 – 102 \times 102)}{96}$  (iv) $1.73 \times 1.73 – 0.27 \times 0.27$  (v) $\frac{(8.63 \times 8.63 – 1.37 \times 1.37)}{0.726}$To do:We have to simplify the given expressions using suitable identities.Solution:Here, we have to simplify ... Read More