Question

Find the value of K : (⅘)² × (⅘)⁵ = (⅘)²k+1​

Answer 1

Answer:

values 3 and -1 .

Step-by-step explanation:

For the given quadratic equation to have equal roots the value of the determinant of the equation

should be equal to zero.

Given equation - 4x²-2(k+1) x+(k+1)

a = 4 , b = -2(k+1) , c = (k+1)

Determinant = b² - 4ac =0

Solving the equation to find the values of k

=> 4(k+1)² - 4 × 4 × (k+1) = 0

=> 4k² + 4 + 8k - 16k -16 = 0

=> 4k² - 8k - 12 = 0

=> k² - 2k -3 = 0

=> k² - 3k + k - 3 = 0

=> k (k-3) +1 (k-3) = 0

=> (k-3) (k+1) = 0

=> k = 3,-1

values 3 and -1 .

Answer 2

${ \underline{ \huge{ \bf{ \red{ \underline{Solution:- }}}}}}$

To find value of K

${ \bf{ \green{ \dashrightarrow{ \purple{ { (\frac{4}{5}) }^{2 } \times {( \frac{4}{5} )}^{5} = {( \frac{4}{5} )}^{2} \times K + 1 }}}}}$

${ \bf{ \green{ \dashrightarrow{ \purple{ \frac{ {4}^{2} }{ {5}^{2} } \times \frac{ {4}^{5} }{ {5}^{5} } = \frac{ {4}^{2} }{ {5}^{2} }\times K + 1 }}}}}$

${ \bf{ \green{ \dashrightarrow{ \purple{ \frac{16}{25} \times \frac{1024}{3125} = \frac{16}{25}\times K + 1 }}}}}$

{ equal term on both side }

${ \bf{ \green{ \dashrightarrow{ \purple{ \cancel{\frac{16}{25} }\times \frac{1024}{3125} = { \cancel{ \frac{16}{25}}}\times K + 1 }}}}}$

${ \bf{ \green{ \dashrightarrow{ \purple{ \frac{1024}{3125} = K + 1 }}}}}$

${ \bf{ \green{ \dashrightarrow{ \purple{ \frac{1024}{3125} - 1 = K }}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: i.e.}$

${ \bf{ \green{ \dashrightarrow{ \purple{ K = \frac{1024}{3125} - 1 }}}} }$

${ \bf{ \green{ \dashrightarrow{ \purple{ K = \frac{1024}{3125} - \frac{3125}{3125} }}}} }$

${ \bf{ \green{ \dashrightarrow{ \purple{ K = \frac{1024 \: - \: 3125}{3125} }}}} }$

${ \bf{ \green{ \dashrightarrow{ \purple{ K = - \frac{2101}{3125} }}}} }$

—› OR ‹—

${ \bf{ \green{ \dashrightarrow{ \purple{ K = - \: 0.67232}}}} }$

i hope it helps you.