Question

Determinati numarul natural x pentru care:
a)x²:(3²)²=2²
b)196:x²=$7^{4}$:7²
c)6²+x²=10²
d)324:$5^{x}$=(2*3²)²

1)8
2)0
3)18
4)2
5)1

Answer 1

Răspuns:

Explicație pas cu pas:

a )

x^2 : ( 3^2 )^2 = 2^2

x^2 : 9^2 = 2^2

x^2 = 9^2 × 2^2

x^2 = ( 9 × 2 )^2

x^2 = 18^2

x = 18

《 Unești a cu 3.

b )

196 : x^2 = 7^4 : 7^2

14^2 : x^2 = 7^( 4 - 2 )

14^2 : x^2 = 7^2

x^2 = 14^2 : 7^2

x^2 = ( 14 : 7 )^2

x^2 = 2^2

x = 2

《 Unești b cu 4.

c )

6^2 + x^2 = 10^2

( triplete pitagoreice )

x^2 = 10^2 - 6^2

x^2 = 100 - 36

x^2 = 64

x^2 = 8^2

x = 8

《 Unești c cu 1.

d )

324 : 5^x = ( 2 × 3^2 )^2

18^2 : 5^x = 2^2 × ( 3^2 )^2

18^2 : 5^x = 2^2 × 9^2

18^2 : 5^x = ( 2 × 9 )^2

18^2 : 5^x = 18^2

5^x = 18^2 : 18^2

5^x = 1

5^0 = 1

x = 0

《 Unești d cu 2.

Answer 2

a)

${x}^{2} \div ( {3}^{2} ) ^{2} = {2}^{2}$

${x}^{2} \div {9}^{2} = {2}^{2}$

${x}^{2} \div 81 = 4$

${x}^{2} = 81 \times 4$

${x}^{2} = 324 = > x = 18$

b)

$196 \div {x}^{2} = {7}^{4} \div {7}^{2}$

$196 \div {x}^{2} = {7}^{2}$

$196 \div {x}^{2} = 49$

${x}^{2} = 196 \div 49$

${x}^{2} = 4 = > x = 2$

c)

${6}^{2} + {x}^{2} = {10}^{2}$

$36 + {x}^{2} = 100$

${x}^{2} = 100 - 36$

${x}^{2} = 64 = > x = 8$

d)

$324 \div {5}^{x} = (2 \times {3}^{2} ) ^{2}$

$324 \div {5}^{x} = (2 \times 9) ^{2}$

$324 \div {5}^{x} = {18}^{2}$

$324 \div {5}^{x} = 324$

${5}^{x} = 324 \div 324$

${5}^{x} = 1 = > x = 0$