If ⁻¹ p+ ⁻¹ q+ ⁻¹ r= , then p²+q²+r²+2 p q r is equal to

Step-by-step solution

We have, aligned &= ⁻¹ p+ ⁻¹ q+ ⁻¹ r= & ⁻¹ p+ ⁻¹ q= - ⁻¹ r & ⁻¹ (p q- 1-p² 1-q² )= - ⁻¹ r & p q- 1-p² 1-q² = ( - ⁻¹ r ) & p q- 1-p² 1-q² =- ( ⁻¹ r ) & p q- 1-p² 1-q² =-r & p q+r= 1-p² 1-q² &(p q+r)²= (1-p² ) (1-q² ) aligned p² q²+r²+2 p q r=1-p²-q²+p² q² p²+q²+r²+2 p q r=1