Question

Form an equation for the following examples.
(i) The sum of a natural number 'x' and its square is 30.
(ii) The product of two numbers 'y' and y$-$3 is 42.
(iii) The sum of a natural number 'x' and its reciprocal is $\frac{37}{6}$.
(iv) The digit at ten's place of a two digit number is greater than the square of digit at unit's place (x) by 5 and the number formed is 61.
(v) The length of a rectangle (x) is greater than its breadth by 3 cm. The area of a rectangle is 70 sq.cm

Answer 1

(i) Let the natural number be x. Then, its square will be x².
Since the sum of the number x and its square is 30, the required equation is x + x² = 30.

(ii) Given: two numbers y and (y – 3)
Since the product of these two numbers is 42, the required equation is y(y – 3) = 42.

(iii) Given: a natural number x. Then, its reciprocal is $\frac{1}{x}$.
Since the sum of the natural number and its reciprocal is$\frac{37}{6}$ , the required equation is $x+\frac{1}{x}=\frac{37}{6}$ .

(iv) Let the digit at the units place of the two-digit number be x.
Since the digit at the tens place is greater than the square of the units place digit by 5, the tens place digit is
(x² + 5)
Since the units place digit is x and the tens place digit is (x² + 5), the number is {10(x² + 5) + x}.
Thus, by the given conditions, the required equation is 10(x² + 5) + x = 61.

(v) Let the breadth of the rectangle be x cm.
Then, its length will be (x + 3) cm.
Thus, the area of the rectangle will be x(x + 3) sq. cm.
We are given that the area of the rectangle is 70 sq. cm.
Thus, the required equation is x(x + 3) = 70.