Solve 3ˣ + 5ʸ = 8; 3ˣ⁺² + 5ʸ⁺¹ = 52.
Answers
Answer:
3*+5y=8;3*+2+5Y+1=52
(1,1)
Step-by-step explanation:
Given :-
3ˣ + 5ʸ = 8;
3ˣ⁺² + 5ʸ⁺¹ = 52.
To find :-
Solve the given equations ?
Solution :-
Given equations are
3ˣ + 5ʸ = 8 ------------------(1)
3ˣ⁺² + 5ʸ⁺¹ = 52 ------------(2)
We know that
a^m × a^n = a^(m+n)
=> 3ˣ×3² + 5ʸ × 5¹ = 52
=> 9 (3ˣ) + 5(5ʸ)= 52 -------(3)
On multiplying (1) with 5 then
=>5( 3ˣ )+ 5(5ʸ ) = 40 ------------------(4)
On subtracting (4) from (3) then
9 (3ˣ) + 5(5ʸ)= 52
5( 3ˣ )+ 5(5ʸ ) = 40
(-) (-) (-)
_______________
4(3ˣ )+ 0 = 12
_______________
We have,
4(3ˣ ) = 12
=> 3ˣ = 12/4
=> 3ˣ = 3
=> 3ˣ = 3¹
=> x = 1
On substituting the value of x in (1) then
3ˣ + 5ʸ = 8
=> 3¹+ 5ʸ = 8
=> 3+ 5ʸ = 8
=> 5ʸ = 8-3
=> 5ʸ = 5
=> 5ʸ = 5¹
=> y = 1
Therefore, x = 1 and y = 1
Answer:-
The solution for the given equations is (1,1)
Check:-
If x = 1 and y = 1 then
3ˣ + 5ʸ
=> 3¹+5¹
=> 3+5
=> 8
LHS = RHS
and
3ˣ⁺² + 5ʸ⁺¹
=> 3¹+² + 5¹+¹
=> 3³+5²
=> 27+25
=> 52
LHS = RHS
Verified the given relations in the given problem.