hello can anyone tell me the answer if this one please .....
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Answers
Answer:
Each root of the equation x² - bx + c = 0 is decreased by 2 resulting in the equation x² - 2x + 1 = 0,find the values of b and c.
\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}Answer:
Given Equation,
\large{ \sf{x {}^{2} - bx + c = 0 }}..........(1)x2−bx+c=0..........(1)
On reducing the roots of above equation by 2,the resulting equation is :
\sf{x {}^{2} - 2x + 1 = 0 }x2−2x+1=0
To find
Values of b and c in the first equation
Consider x² - 2x + 1 = 0
\begin{lgathered}\sf{x {}^{2} - 2x + 1 = 0 } \\ \\ \leadsto \: \sf{x {}^{2} - x - x + 1 = 0 } \\ \\ \leadsto \: \sf{x(x - 1) - 1(x - 1) = 0} \\ \\ \leadsto \: \sf{(x - 1) {}^{2} = 0 } \\ \\ \leadsto \: \boxed{\sf{x = 1}}\end{lgathered}x2−2x+1=0⇝x2−x−x+1=0⇝x(x−1)−1(x−1)=0⇝(x−1)2=0⇝x=1
We get 1 as the root of the second equation
》 3 would have been the root of the first equation
\begin{lgathered}\: \sf{x = 3} \\ \\ \rightarrow \: \sf{(x - 3) = 0}\end{lgathered}x=3→(x−3)=0
Consider x² - bx + c = 0,product of its roots would give us the equation back.
\begin{lgathered}\sf{(x - 3)(x - 3) = 0} \\ \\ \implies \: \sf{x(x - 3) - 3(x - 3) = 0} \\ \\ \implies \: \sf{x {}^{2} - 3x - 3x + 9 = 0 } \\ \\ \implies \: \underline{ \boxed{\sf{x {}^{2} - 6x + 9 = 0 }}}................(2)\end{lgathered}(x−3)(x−3)=0⟹x(x−3)−3(x−3)=0⟹x2−3x−3x+9=0⟹x2−6x+9=0................(2)
Comparing equations (1) and (2),we get :
b = 6 and, c = 9
Answer:
He can measure 4kg mangoes in this way-
He can place a weight of 6kg on one scale and then place a 2kg weight on another one... He can start putting mangoes bit by bit till both the scales are balanced.
He can measure 3kg oranges in this way-
He can place 5kg on one scale and then place 2kg on another one... He can start placing oranges one by one till both the scales are balanced.
Hope it helps!
Thank You.