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Standard XII
Mathematics
Definition of Functions
Prove that th...
Question
Prove that the values of x obtained from the equations ax²+by²=1 and ax+by=1 will be equal if a+b=1.
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Solution
Given a+b=1=>b=1-a
From equation (1)
ax^2+by^2=1
=>x^2 = (1-(1-a)y^2)/a
= ((a-1)y^2+1)/a
From equation (1)
ax+by=1
=>x =(1-(1-a)y)/a
=((a-1)y+1)/a
=>x^2 =((a-1)^2y^2+1-2(a-1)y))/a^2
simplyfying this you get the answer of x^2 in equation 1
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