Question

Find the value of x, if 6x = 23² - 17²​

Answer 1

Solve using identity

Using algebraic identity makes it easy to calculate and to solve fastly!

a² - b² = (a-b)(a+b)

Now, put in the values of constant a and b

6x = (23 + 17)(23-17)

6x = (40)(6)

6x= 40 × 6

cancel 6 both sides

x = 40

$\rule{200}{1}$

Answer x = 40

Answer 2

Given:

6x = 23² - 17²

Now,

23² - 17²

Of the form a² - b²

=(23+17)(23-17)

=40×6

=240

Thus,

$6x = 240 \\ \\ \implies \: x = \frac{240}{6} \\ \\ \implies \: \huge \boxed{x = 40}$

•Identities used:

a² - b² = (a+b)(a-b)

•Some important identities:

(a + b)²= (a+b)(a+b)=a² +2ab + b²

(a - b)² = (a-b)(a-b)=a² -2ab + b²

(x+a)(x+b) = x² +(a+b)x + ab