To do:We have to evaluate the given expressions using the formula for squaring a binomial.Solution:Here, we have to find the squares of some large numbers. We can find the squares of multiples of $10^n$ easily. So, express the given numbers as the sum of multiples of $10^n$ and other numbers. ... Read More

Given:$x^2 + y^2 = 29$ and $xy = 2$To do:We have to find the value of(i) $x + y$(ii) $x - y$(iii) $x^4 + y^4$Solution:The given expressions are $x^2 + y^2 = 29$ and $xy = 2$. Here, we have to find the value of (i) $x + y$ (ii) $x - ... Read More

Given:$2x + 3y = 14$ and $2x - 3y = 2$To do:We have to find the value of $xy$.Solution:The given expressions are $2x + 3y = 14$ and $2x - 3y = 2$. Here, we have to find the value of $xy$. So, by squaring and subtracting using the identities $(a+b)^2=a^2+2ab+b^2$ and $(a-b)^2=a^2-2ab+b^2$, we ... Read More

Given:$x + \frac{1}{x} = 12$To do:We have to find the value of $x - \frac{1}{x}$.Solution:The given expression is $x + \frac{1}{x} = $. Here, we have to find the value of $x^4 + \frac{1}{x^4}$. So, by squaring the given expression and using the identities $(a+b)^2=a^2+2ab+b^2$ and $(a-b)^2=a^2-2ab+b^2$, we can find the required ... Read More

Given:$x + \frac{1}{x} = 9$To do:We have to find the value of $x^4 + \frac{1}{x^4}$.Solution:The given expression is $x + \frac{1}{x} = 9$. Here, we have to find the value of $x^4 + \frac{1}{x^4}$. So, by squaring the given expression and using the identity $(a+b)^2=a^2+2ab+b^2$, we can find the required ... Read More

To do:We have to find the values of the given expressions.Solution:Here, we have to find the values of the given expressions. So, simplifying the given expressions using the identities $(a+b)^2=a^2+2ab+b^2$.............(I) and $(a-b)^2=a^2-2ab+b^2$.............(II) and substituting the values of $x$ and $y$, we can find the required values.(i) The given expression is $16x^2 + ... Read More

Given:$3x + 5y = 11$ and $xy = 2$To do:We have to find the value of $9x^2+25y^2$.Solution:The given expressions are $3x + 5y = 11$ and $xy = 2$. Here, we have to find the value of $9x^2+25y^2$. So, by squaring the given expression and using the identity $(a+b)^2=a^2+2ab+b^2$, we ... Read More

Given:$x – y = 7$ and $xy = 9$To do:We have to find the value of $x^2+y^2$.Solution:The given expressions are $x – y = 7$ and $xy = 9$. Here, we have to find the value of $x^2 + y^2$. So, by squaring the given expression and using the identity ... Read More

Given:$x + y = 4$ and $xy = 2$To do:We have to find the value of $x^2 + y^2$.Solution:The given expressions are $x + y = 4$ and $xy = 2$. Here, we have to find the value of $x^2 + y^2$. So, by squaring the given expression and using ... Read More

Given:$x - \frac{1}{x} = 3$To do:We have to find the values of $x^2 + \frac{1}{x^2}$ and $x^4 + \frac{1}{x^4}$.Solution:The given expression is $x - \frac{1}{x} = 3$. Here, we have to find the values of $x^2 + \frac{1}{x^2}$ and $x^4 + \frac{1}{x^4}$. So, by squaring the given expression and using the ... Read More