Question

The number of pair (a,b) of positive real numbers satisfying a^4+b^4<1 and a^2+b^2>1 is

Answer 1

Answer:

Step-by-step explanation:

According to the given situation,0<a4+b4<1<a2+b2⟹a4+b4<a2+b2⟹0<a2(a2−1)<b2(1−b2)⟹b2(1−b)(1+b)<0;a2(a−1)(a+1)>0⟹a∈(−∞,−1)∪(0,1);b∈(−1,0)∪(1,∞)

But, in particular, if we choose a=−1/2,b=1/2,then a4+b4=1/16+1/16=1/8<1 and a2+b2=1/4+1/4=1/2<1.Which contradicts the given condition a2+b2>1

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