Question

Please tell my school exam's question is this​

Answer 1

Answer:

39 and 38

Step-by-step explanation:

let the 2 consecutive numbers be x and x-1

( square = *)

x* - ( x-1)* = 77

x* - ( x*+1-2x ) = 77

x*-x*-1+2x = 77

2x = 78

x = 39

x-1 = 38

Answer 2

QUESTION :–

▪︎ If the difference between square's of two consecutive natural number is 77 then the numbers are –

(a) 37 , 38

(b) 38 , 39

(c) 39 , 40

(d) 40 , 41

(e) 35 , 36

ANSWER :–

GIVEN :–

• Difference between square's of two consecutive natural number is 77.

TO FIND :–

• Numbers = ?

SOLUTION :–

• Let two consecutive natural number is 'x' and 'x+1'.

▪︎ According to the question –

$\\ \implies{ \bold{ {(x + 1)}^{2} - {(x)}^{2} = 77 }}$

▪︎ Using identity –

$\\ \: \: \longrightarrow \: \: {\overbrace {\underbrace{ \bold{ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab }}}}$

• So that –

$\\ \implies{ \bold{( {x}^{2} + 1 + 2x ) - {(x)}^{2} = 77 }}$

$\\ \implies{ \bold{ \cancel{{x}^{2}} + 1 + 2x - \cancel{{x}^{2}} = 77 }}$

$\\ \implies{ \bold{ 1 + 2x= 77 }}$

$\\ \implies{ \bold{ 2x= 77 - 1 }}$

$\\ \implies{ \bold{ 2x= 76 }}$

$\\ \implies{ \bold{ x= \cancel\dfrac{76}{2} }}$

$\\ \implies \large{ \boxed{ \bold{ x= 38}}}$

▪︎ The numbers are ( 38 , 38 +1 ) = (38 , 39)

● Hence Option (B) is correct .